5

Write an equation of the tangent Ilne " to the graph ofy = f(x) at the point on the graph where has the indicated value _ fx) = (2x ? , 3x - 2)(-4x + I*-0 y-4*...

Question

Write an equation of the tangent Ilne " to the graph ofy = f(x) at the point on the graph where has the indicated value _ fx) = (2x ? , 3x - 2)(-4x + I*-0 y-4*+2 Y = TIx + 2 yix-2 0y-I1x - 2

Write an equation of the tangent Ilne " to the graph ofy = f(x) at the point on the graph where has the indicated value _ fx) = (2x ? , 3x - 2)(-4x + I*-0 y-4*+2 Y = TIx + 2 yix-2 0y-I1x - 2



Answers

Use (2) to find the slope of the tangent line to the graph of the function at the given value of $x$. Find an equation of the tangent line at the corresponding point. $f(x)=-2 x^{3}+x, x=2$

For the following exercise we want to find the slope of the tangent line to the graph with a given value of X. And then we're gonna find an equation of the tangent line at the corresponding point. Um So what we have is half of axe april's X squared minus six. And using what we know the slope of the tangent line to the graph at any given value X Is going to be two x. But now we know that X equals three. So that means that six is going to be the slope. So we have y equals six. Act be And since we know that when x equals three Y equals zero We can plug in a three here And why it was zero here That will give us B equals negative 18. So we see it x equals three. Um What we end up getting is that the graph matches up? This is actually gonna be when X equals three. The other one equals 33 of 18. So it's actually 15. You can point to it see that it intersects right at three and that's where it has the tangent line

Okay, We've been asked to find the tangent plane. Tow this function at the point. Negative one, too. First of all, noticed that f of X Y is equal to Z, right? And that f of negative one, too, is equal to two minus four times solar negative. 16 zip plus 16 which is 18. Okay, so this is the the point. Negative 1 to 18. Okay, so we're gonna rewrite our function as a level curb of a function of three very votes. So this is ah ah of X. Why minus Z, which is two x squared, minus four x y squared minus z. Okay, so now we'll find the Grady and of this function. So the Grady int of capital if of X y z is equal to the partial with respect to X is for X minus for y squared. The parcel with respect to why is minus eight. Fix why? And the parcel with respect. Izzie is negative one. Okay, so we need to evaluate the Grady int at our point, which is negative. One, two, 18. So this is net negative. Four minus 16. Negative. Eight times negative. One comes negative to positive. 16 negative one. So this is negative. 20 16 and negative. Okay, so the equation of the tangent plane is negative. 20 times X plus one plus 16 times. Why? Minus two minus Z minus 18. This is equal to zero. Okay, So noticed that, um, the direction numbers right in front of each term. And that the point Negative. 12 in positive 18. It's right there. Okay, so let's distribute. So this is minus 20 eggs minus 20 plus 16. Why? Minus 32 minus Z plus 18 is equal to zero. So this is negative. 20 X plus 16 wine minus Z is equal to 30 four. And this is the equation of the tangent plane.

Hello, everyone. We're trying to find the equation off the tension lines. The graph of FX at the indicated xlu. So we have F X is equal to x cube. I was very negative. X cubed plus four X squared. Oh, just for X. A negative, x cubed plus four x and it's going to be an X is equal to two. First we take the slope of this so we get this is equal to the derivative aftereffects is equal to three x squared because of the general plus four X. And so now that we have the derivative, we can find the slope. So we're going to plug this into our derivative to get our slopes of the F prime. The rate of change at X is equal to two is equal to negative 12 plus four, which is equal to negative eight sonar equation we're going to have Why is ableto mx plus baby adviser with a negative eight x plus b? So now where's that fine be? And we already have our value. Um, so first, let's get a quick coordinate point. Um, so we have X is equal to two, and we're going to plug this into this equation now, So we get effort to is equal to negative off to Cube, which is too negative. Eight plus, uh, four times two is eight equals zero. So this causes the 00.2 comma zero. So we're going to plug this into our bicycle to MX plus B. So we get zero is equal to negative 16 x. It's a negative 16 plus B. And we get B is you go to 16. So we have our slope and we ever were intercepted. Somehow we have all we need to create our equation. You have? Why is equal to M, which is a slope Negative. Eight, uh, ex plus plus 16. Thank you for watching. And I hope this helps.

Hello everyone. So in this question we're going to solve for the equation of the tangent line to the given function at a given. Excellently. So in order to find the equation of potential. Fine we need to find the slope and the Y intercept so recalled that we can find the slope by funny derivative and then plugging the X value into the derivative which will give us the slope of the tangent line at the excel. And then we can find the Y intercept by then plugging in a value of X and Y on the give it function. So are given function is X squared times X minus one. Cute. And we have to solve at the given X value to. So first we have to find the derivative of our original function. So we should use the product rule here. The private pool states that if we have a function F. Palace function G. We found derivative. Bye Function F. five times G plus F times cheaper. So here it is equal to X square And G is equal to X -1. Cute. A friend was easy to find. It's just to excuse in the power rule and G. Prime what to use the style ted rule. So let's take the outer function to the queue. Use the power rule. Leave the inter function alone and three minutes 1 is Leaves us to put the power of two times the derivative of the inner function which is X minus war. And that is what and plug that into the formula for the product rule. So F prime is two X times G which is x minus one cubed us. F which is X squared times G. Prime which is three. That's X -1 squared. Now in order to find the slope of the tangent line at the given X. Valley ought to do is plug in the X value just to into the derivative expression. So We have two times 2 times two minus one. Cute plus two squared times three. That's 2 -1 squared. Stood Algebra. So four times two minutes 1, 1, 4 plus four times three times one. Just 12 equal to 16. So that is our slope with the tension line. So here's what are tangent line equation looks like so far after we plugged in slope, I just need to find the Y intercept by finding a point X. Y. That lies on the tangent line. So we know the tangent line intercepts with our original function. Um At the point that we specified which has x value of two. So now we just need to find the corresponding why valley on our original function That corresponds with x equals two. So it's quite to end The original function. So you get to square times 2 -1 cubed, Which is equal to four. So let's plug in or for why? And then two for X. and so for being so busy with the four, one is 32 Which is equal to -28. So the final equation is y equals 16 X -28.


Similar Solved Questions

5 answers
Problem 45.4. Show312 2t cos? (a"x) + sin? (a"x) - 467,)) + +8n where & - 0 as n - Hint: Use An - Ca (x) and Tn - Ca (x) Using %2 < 10 and a > 12, we get 312 914 4x2 9.100+4.16.10 1540 225, 7)_ 4)' (2) (a 16. 121 121 16.121 1936 Problem 45.5. Derive a contradiction_
Problem 45.4. Show 312 2t cos? (a"x) + sin? (a"x) - 467,)) + +8n where & - 0 as n - Hint: Use An - Ca (x) and Tn - Ca (x) Using %2 < 10 and a > 12, we get 312 914 4x2 9.100+4.16.10 1540 225, 7)_ 4)' (2) (a 16. 121 121 16.121 1936 Problem 45.5. Derive a contradiction_...
5 answers
(1 point) Book Problem9y 17 dy.Use the Table of Integrals in the back of your textbook t0 evaluatePerform the substitutionUse formula number9y2
(1 point) Book Problem 9y 17 dy. Use the Table of Integrals in the back of your textbook t0 evaluate Perform the substitution Use formula number 9y2...
5 answers
Find the eigenvalues and eigenvectors of A and A2 and 4-1 and A + 4:2 42 _ 5 _4 A=[-3 -27 and -4 5
Find the eigenvalues and eigenvectors of A and A2 and 4-1 and A + 4: 2 42 _ 5 _4 A=[-3 -27 and -4 5...
5 answers
Cyy & +5 7 246fs5
Cyy & +5 7 2 46 fs 5...
5 answers
Pisuus AicoritPioranKeneualempoint Asn #na64le.umieaina conslant s Rdoct Me2s Eauta leruand nennrastuem zelo veoch Iic robmion ofine]n Knaln Ine Val Amt?stnetchau - Muers DcrabmnraTIATeTCosJENEeanduadeee_ tundcn olthc vanati ( #Inmg gereral"oln Ceut cos(Ar) Cze"" sin(%)
Pisuus Aicorit Pioran Keneualem point Asn #na64le.umieaina conslant s Rdoct Me2s Eauta leruand nennrastuem zelo veoch Iic robmion ofine]n Knaln Ine Val Amt? stnetchau - Muers Dcrabmnra TIAT eTCos JENEeanduadeee_ tundcn olthc vanati ( #Inmg gereral"oln Ceut cos(Ar) Cze"" sin(%)...
5 answers
A photograph measures 8 inches by 6 inches, ad is surrounded by mat The mat has Ihe same width on all sides of the photograph. The photograph and the mat are put into a glass photo frame which just covers the outside of tne mat: If the area of the glass surface is 120 square inches, algebraically determine the width of the mat to the nearest tenth of an inch [3 marks] 'Write your final answer as a sentence
A photograph measures 8 inches by 6 inches, ad is surrounded by mat The mat has Ihe same width on all sides of the photograph. The photograph and the mat are put into a glass photo frame which just covers the outside of tne mat: If the area of the glass surface is 120 square inches, algebraically de...
5 answers
Question 15Let &(0, 2,5) and 6 = (4,0,1). Find the angle between the vector (in fadians)
Question 15 Let & (0, 2, 5) and 6 = (4,0,1). Find the angle between the vector (in fadians)...
5 answers
2 2 1 IJH 8 1 1801 113
2 2 1 IJH 8 1 1 8 0 1 1 1 3...
5 answers
For the following teaction with the following energy curve:H-geH-o-cBStaning MaloralaProduclWhat &cs Hamonds postulatc Imply about thc stnrchuc of thc transition slalc?~0+8XLD) Hannonds postubic dxs not imply Jaything about thcatnnc of tc transibou saicHINT: Is this an early or late transition state?
For the following teaction with the following energy curve: H-ge H-o-c B Staning Malorala Producl What &cs Hamonds postulatc Imply about thc stnrchuc of thc transition slalc? ~0 +8X L D) Hannonds postubic dxs not imply Jaything about thcatnnc of tc transibou saic HINT: Is this an early or late t...
5 answers
Solve this as a Linear First Order DE Consider the differentialequation: (x2 + 1) dy/dx + 3xy = 6x
Solve this as a Linear First Order DE Consider the differential equation: (x2 + 1) dy/dx + 3xy = 6x...
5 answers
A1OOUC point charge having = mass of 2.50 grams shot into _ region where there is. very strong magretic field The particke is initially travcling parallel to the positive axiswith speed of 500 IV/s. The magnetic feld is directed such that its x-componentis 4.00 Tesla its Y-component is OO Tesla. and its_ component is 4.00 Tesla_ Whal magnitude of the acceleration of the particle? Neglect gravity:2.50 1Vs?125 01321750VY?250 ms?150 mszL00 IVs"500 mus2100 mVs?
A1OOUC point charge having = mass of 2.50 grams shot into _ region where there is. very strong magretic field The particke is initially travcling parallel to the positive axiswith speed of 500 IV/s. The magnetic feld is directed such that its x-componentis 4.00 Tesla its Y-component is OO Tesla. an...
4 answers
Question 30At 250C, what IS the pH ofa 0.10 M Ca(OH)2 solution?13.0013.300.701.00
Question 30 At 250C, what IS the pH ofa 0.10 M Ca(OH)2 solution? 13.00 13.30 0.70 1.00...
5 answers
NllnsweredA cell membrane has a capacitance C=3.04 x 10" FIfthe potential difference across the membrane is V = 0.15 Volt; the electric energy U (in joule) stored in the membrane equalsut 0f 4 00uestiona) 3.42x [0-9 6) 7.08 x 10 : c) L.0x 10 " d) 7.97x [0-9
nll nswered A cell membrane has a capacitance C=3.04 x 10" FIfthe potential difference across the membrane is V = 0.15 Volt; the electric energy U (in joule) stored in the membrane equals ut 0f 4 00 uestion a) 3.42x [0-9 6) 7.08 x 10 : c) L.0x 10 " d) 7.97x [0-9...
5 answers
Find integers m and n such thatgcd(a,b) am + bn.
find integers m and n such that gcd(a,b) am + bn....
5 answers
Consider the differential equationx'(a) Solve the differential cquation(b) Convert the problem into a second order linear ODE with constant coefficients.
Consider the differential equationx' (a) Solve the differential cquation (b) Convert the problem into a second order linear ODE with constant coefficients....

-- 0.021724--