5

Q2/ Answcr two only from the following:(10 Marks )(a) Consider the following graph of a function y = f(x):Find Df' (x) and R;' (x): Furthermore, is Rolle ...

Question

Q2/ Answcr two only from the following:(10 Marks )(a) Consider the following graph of a function y = f(x):Find Df' (x) and R;' (x): Furthermore, is Rolle $ Theorem applies for f (x) Whose graph is given above On the interval [1,5]2 Explain that.

Q2/ Answcr two only from the following: (10 Marks ) (a) Consider the following graph of a function y = f(x): Find Df' (x) and R;' (x): Furthermore, is Rolle $ Theorem applies for f (x) Whose graph is given above On the interval [1,5]2 Explain that.



Answers

Rolle's Theorem Determine whether Rolle's Theorem applies to the following functions on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem. $$f(x)=x(x-1)^{2} ;[0,1]$$

Number seven giving function is continues and the French able on a given interpret. So check that beats the u zero U minus. One squared and if one is a quick 11 minus one is where we get for our own theater can be applied for and giving function on again into, so we need to find points in the given Interpret where dash off X is equal to zero. Financial X is equal X dash X minus one. We're plus its dash Knicks minus one. Yes, which is equally true. X minus one. It's where lost X who x minus one, which is equal to X minus one. Lying by its minus one plus two X equals X minus 13 X minus one. So now we set a bunch of ex Is it with you? Is with convenience store X equals one and excess. It was fair. Sense X equals one is a boundary. Points off. Give it closed in Terrible we can't used so See it would

Today we're going to solve problem number one here. This problem therefore X equal fine minus who elects plus 13 x square. So it is a pole normal function. It is always different shovel and continuous F off one equal toe five minus trolling the one plus 13 into one square, which is the Goto minus four. And for three equal toe fi minus. Well, the window three plus continuing. Do sorry. Here it's tree story, your Question Street three into three square, which is ableto minus food. So f off one he could do 43 Rose Cheramie is applicable in the clothes You never want to come out. Three differentiator for effects after projects equal toe minus 12 plus six x so f d I. C equal to zero minus two yl plus 60 equal to zero c equals toe. Thank you

Okay, let's picture this situation. So we have some function f and we know it lies entirely in quadrant too. So maybe it looks something like this so noticed that the coordinate pairs would always have Ah, Puskas me A negative X coordinate, followed by a positive y coordinate. So that means for the inverse we're going to have a positive X coordinate, followed by a negative y coordinate. And also remember that these were going to be reflections across the line. Y equals X. So we're going to end up with something like this, and that means f inverse is going to be in the fourth quadrant.

So because we don't actually have the graph available, let's consider different possibilities. So if we have for example the graph X. I'm cubed -2X. For example, museum in here and look at this and we want to know intervals. How much is concave uh huh. How much is increasing? Well that's going to be increasing from here to here and that starts decreasing from here to here and it's increasing from there and not further. Then we want to know where it's decreasing. So we already defined that. Then we want to know um when it's concave uh So we see it's going to be concave up once it reaches this inflection point and it goes up like this. But then to be concave down to the left of that inflection point. So we see that the inflection point is going to be located right here because that's when the graph switches from concave down to con cuba. So that's our final answer.


Similar Solved Questions

5 answers
(15 POlla) Find the 0-1,Gnd atulue mbltaum % J6 =The farmer wante enciose Fectalle faiter has 1200 meters fencing (I0 points) Lhe FVCE. Find the dituensOnS field bordering & rivet; with no fencing ueeded along ( gular to maximize the area of the field the field
(15 POlla) Find the 0-1, Gnd atulue mbltaum % J6 = The farmer wante enciose Fectalle faiter has 1200 meters fencing (I0 points) Lhe FVCE. Find the dituensOnS field bordering & rivet; with no fencing ueeded along ( gular to maximize the area of the field the field...
5 answers
70. Proof Prove that if A, B, and € are square matrices and ABC L,then B is invertible and B-1 CA.
70. Proof Prove that if A, B, and € are square matrices and ABC L,then B is invertible and B-1 CA....
5 answers
11.1 Explain why the default state in prokaryotes is ON and in eukaryotes; OFF11.2 Describe the experiment that allowed researchers to identify the promoter proximal regions11.3 Know the structural and regulatory genes of the GAL system; how they are distinguished (identified) and how they act (particularly regarding any of the regulatory genes} 11.4 Describe what is meant by modular nature of a protein; and how this property is identified experimentally:
11.1 Explain why the default state in prokaryotes is ON and in eukaryotes; OFF 11.2 Describe the experiment that allowed researchers to identify the promoter proximal regions 11.3 Know the structural and regulatory genes of the GAL system; how they are distinguished (identified) and how they act (pa...
5 answers
3} 1 = 1 { tel Vi helaht li tu6 1 1 1 1 { 1M {BlockEquilibrium position of spring # 1 Acceleration 1 = 1 Enenton 1 gravity; compressed 1{ V
3} 1 = 1 { tel Vi helaht li tu6 1 1 1 1 { 1 M { Block Equilibrium position of spring # 1 Acceleration 1 = 1 Enenton 1 gravity; compressed 1{ V...
5 answers
(c) What Is the sign of the leadlng coefficlent of f?Select One(d) Which of the followingpossibillty for the degree of {? Choose all that apply.
(c) What Is the sign of the leadlng coefficlent of f? Select One (d) Which of the following possibillty for the degree of {? Choose all that apply....
5 answers
Use an identity to find the exact value of the expression. sin '(6+4)sin 3 (Type an exact answer; using radicals as needed Rationalize all denominators )
Use an identity to find the exact value of the expression. sin '(6+4) sin 3 (Type an exact answer; using radicals as needed Rationalize all denominators )...
5 answers
Lett1.4101Precious Gastin; Attempi4} The llmit Is 5,Question 9 (1 point)SawdUse the figure shown to answer the following question aboutro} What Is thel /()?0m The 5 Umjt clacs not exist,21 Tha imit [9The Ilmlt /5 -Tna Wmjt [,04Question 10 (1 polnt)
Lett1.4101 Precious Gastin; Attempi 4} The llmit Is 5, Question 9 (1 point) Sawd Use the figure shown to answer the following question aboutro} What Is thel /()? 0m The 5 Umjt clacs not exist, 21 Tha imit [9 The Ilmlt /5 - Tna Wmjt [,04 Question 10 (1 polnt)...
5 answers
List the allowed quantum numbers $m_{l}$ and $m_{s}$ for the following subshells and determine the maximum occupancy of the subshells:a. $2 p$b. $3 d$c. $4 f$d. $5 g$
List the allowed quantum numbers $m_{l}$ and $m_{s}$ for the following subshells and determine the maximum occupancy of the subshells: a. $2 p$ b. $3 d$ c. $4 f$ d. $5 g$...
5 answers
(Trla %r False: For ay statistical hypothesis Icst the P value [5 less than the significance Ievcl Uaethesb @ then we would Fail to Reject the Nul0True0 False
(Trla %r False: For ay statistical hypothesis Icst the P value [5 less than the significance Ievcl Uaethesb @ then we would Fail to Reject the Nul 0True 0 False...
5 answers
Table of values of an increasing function f is shown Use the table to find lower and upper estimates for lower estimate upper estimatef(x) dx:101418 22 26 30f(x)~13 -5-1
table of values of an increasing function f is shown Use the table to find lower and upper estimates for lower estimate upper estimate f(x) dx: 10 14 18 22 26 30 f(x) ~13 -5 -1...
5 answers
Consider thc following problem:The height h(t) of a rectangle is increasing at a rate of 1l cm/day and the width w(t) of the rectangle is decreasing at a rate 0f 9 _ cm /day.At a certain instant to, the height is 3 Cm and the width is 8 cm What is the rate of change of the area A(t) of the rectangle at that inslant?Match each expression #Ath ies units;CIIcm/day cm? cm" /dayh(t)w(to )
Consider thc following problem: The height h(t) of a rectangle is increasing at a rate of 1l cm/day and the width w(t) of the rectangle is decreasing at a rate 0f 9 _ cm /day.At a certain instant to, the height is 3 Cm and the width is 8 cm What is the rate of change of the area A(t) of the rectangl...
5 answers
Use the concept of the area of a triangle discussed in Exercises $39-44$ to determine whether the three points are collinear.$$(-1,-4),(3,8),(6,17)$$
Use the concept of the area of a triangle discussed in Exercises $39-44$ to determine whether the three points are collinear. $$(-1,-4),(3,8),(6,17)$$...
5 answers
Solve the following Indefintte Integral:J(+ dx
Solve the following Indefintte Integral: J(+ dx...
5 answers
Ut T : iR' > iR? L +L K~ 4 4 +(6^> 6(kat/0 u&~4 +d T ( x, *)a (31,-*, 47,1*11 Xi + 1) SLf irz Lu 6ajos Pa}e (2,u)] ~ ir} Le> L > F' ={ox (19),(%0)5 ^)find A Katn "a atatra^ oF T Kll serrt4 +o k 6^t f 6) U v- (2 6) . Comr-h CTca)lp'
Ut T : iR' > iR? L +L K~ 4 4 +(6^> 6(kat/0 u&~4 +d T ( x, *)a (31,-*, 47,1*11 Xi + 1) SLf irz Lu 6ajos Pa}e (2,u)] ~ ir} Le> L > F' ={ox (19),(%0)5 ^)find A Katn "a atatra^ oF T Kll serrt4 +o k 6^t f 6) U v- (2 6) . Comr-h CTca)lp'...
5 answers
If (Gn)? _ (an-1)(an+1) = (~2)" for n 21 and Qo = 01= ] then 43 2 ) 0 b ) 5 c)-3 d ) 1 noneb
If (Gn)? _ (an-1)(an+1) = (~2)" for n 21 and Qo = 01= ] then 43 2 ) 0 b ) 5 c)-3 d ) 1 none b...
5 answers
4(s+4) [(+17+4] Zes 7143 210. If()= 2 elmt+cos4tMML1, re)e(-4)"412 f()we 'tsin2t"69*6- 2 54s 6+9)f()ecos6-)) +36J1s f() wsin2tsin St5+3rW)= sin? ,
4(s+4) [(+17+4] Zes 7143 2 10. If()= 2 elmt+cos4t MML1, re)e(-4)" 412 f()we 'tsin2t "69*6- 2 54s 6+9) f()ecos 6-)) +36 J1s f() wsin2tsin St 5+3 rW)= sin? ,...
5 answers
[12 points] A 2D plane curve is defined by € : r(t) = ( Acos(wt)A sin(@t) ) _Verify by direct computation that Ili(t)ll constantDetermine the formula for 7()Verify by direct computation that {'(C) is orthogonal to 7(0) .Cextijue (btt; {nnula Br 7(0) aud thc constanr & foe which 7"(0) + B 'F(0) =6
[12 points] A 2D plane curve is defined by € : r(t) = ( Acos(wt) A sin(@t) ) _ Verify by direct computation that Ili(t)ll constant Determine the formula for 7() Verify by direct computation that {'(C) is orthogonal to 7(0) . Cextijue (btt; {nnula Br 7(0) aud thc constanr & foe which 7...

-- 0.021381--