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Find the slope of the tangent to the graph of the function flx) = %*at Xo = 1...

Question

Find the slope of the tangent to the graph of the function flx) = %*at Xo = 1

Find the slope of the tangent to the graph of the function flx) = %* at Xo = 1



Answers

Find the slope of the tangent line to the graph of $f$ at the given point. Graph $f$ and the tangent line. $$f(x)=-2 x+1 \text { at }(-1,3)$$

Hey, guys. And this problem, we're gonna be finding the slope to the line Tangent to the graph f of X equals E to the X at the 0.1 So we can go ahead and take the derivative. The derivative will give us the slope to the line tangent at any given point so we can take the derivative the derivative of either the X is you did the X and I can prove that. So whatever we have the for meat of the U, the derivative is simply eat of the u times. Do you the X We have e to the X take the derivative. That's gonna B e to the x times. Do you d x, the derivative of X is one. So overall we have either the ex. So we're back to our problem. We have you to the X. At 01 we can simply plug in our X value. We don't have to worry about the why, since we're only finding the slope here so we can write DF DX and you can denote it like this. I like to read a line and then at the top xy xy go zero take you to the zero and that is one so we can write m equals one

Okay, so we look to find a spoke over tangent line. Given our xlu, what s Time X is given to be one that means are a value is also equipped to button So it's find are following slope are using this equation here But we have other wrecks and then we need up great Well, we said that are a value is equal to one So we got one cube which is equal to one and then we also have X minus a which is equal to X minus 81 Um, now let's put this into our equation here. So we said are a volley was one We have anthrax that's X cubed minus a one over X minus one. So let's recall doubts here leukemia are one as one cubed and then we have the difference of two cubes, so we can factor this accordingly. So that's going to be X minus one times x squared plus x and n plus one all over X minus one. And now let's cancel out our like terms and used Rex up to find a falling limit. So we have one squared plus one. What's one. So we shoot out the slope of our following 10. Deadline is equal to three

Hello everyone. So in this question were given a function 1/3 X plus one squared. And we have to solve for the slope of the tangent line to this function at X equals zero. Be good to review that. The definition of the derivative is that it is the equation for the slope of the tangent line. So basically any value of X. That you plug into. The derivative of a function gives you the slope of the tangent line at that specific value of X. So the first thing we're going to want to do is find a derivative of our functions. So um I will just start by writing this function as three X plus one to name to power. I just found that it makes it easier for me to look at how to differentiate it. So it looks like we're going to have these a changeable here. Since we have an outer function let's call fx which is the inter function G X two. Power of negative two. And then this inner function is three X plus one. So let's apply the chain rule. We first take the derivative of the outer function which is Yeah which is native to three. X plus one. Using power rule. And then 8: -1 is -3. Then we multiply by the derivative of the inside function which is three Experts 1. So that directive is three. And just simplify it. We can multiply this constant together. So the derivative of our function is negative six over three. x plus one. Cute. All right. And then in order to solve for the slope of the tangent line at X equals zero. We just have to plug in X equals zero. So if you plug in X equals zero. To the derivative equation negative six over three times zero plus one cubed is equal to negative 6/1. It's equal to -6. So that is the slope of the tangent line To this function at X equals zero.

Mhm. In the infusion Human function is if X is equal to X cube plus one, multiplied by X square minus two. Now in the question it is asking to find this globe and uh tangent line. Eight point given in the kitchen duties. Two comma 18. So this is a coordinate off point. So we have to find the slope and tendon line for finding slow. First we have to find Fds X means sterility of function. F X so pushed. I'm using a rule that is a called product rule. So according to this rule, the derivative of FX means Fs X will be equal to X cubed plus one times of differentiation of X square differentiation means D by D X of X squared minus two. Then plus sign than actual minus two differentiation of means D by D X of ask you plus one. No we have to simplify this exhibition. Yeah. So after following this expression I will get FDS X. That will be equal to X cubed plus one. And differentiation of X where minus two will be two X then plus X squared minus two. And differentiation of X cubed plus one will be three X squared. Now I have to find the globe at access card to and why is cooled to 18 So you place X by two. Then the value of slope that will be equal to have death two is equal to. So replacing X by two. Then it will be excuse me. Eight plus one. Multiplied by two weeks means four plus X. Well minus two means four minus two. That will be equal to two times of three X square missed three times of four. That will be equal to do well. So after seeing solving this I will get slope F Death to that will be equal to 60. So this is the value of slope. Now I'm trying to find the tangent line equation. So as we know the general formative tangent line equation when coordinated X one by one. Then the question is why minus y one is equal to M x minus x one. Here X one Y one is a coordinate and M is a slow support. The value of X one Y one that will be equal to two comma 18 and the value of em that will be equal to 16 30 60. So it means tangent line equation is why minus 18 is equal to 16 times of x minus two. So after solving this, I will get the value of tangent line equation. So the tangent line equation is yeah why is equal to 60 x minus 102. So this is the equation for tangent line and uh value of slope will be equal to 50. Thank you.


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