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Find f' (x) and find the value(s) of where the tangent line is horizontal;, f(x) =x" (x - 10)3 {(= Select the correct choice below and; if necessary; fill...

Question

Find f' (x) and find the value(s) of where the tangent line is horizontal;, f(x) =x" (x - 10)3 {(= Select the correct choice below and; if necessary; fill in the answer box within your choice.0 A The tangent line is horizontal at x = (Use comma t0 separate answers as needed 0 B: The tangent line is never horizontal;

Find f' (x) and find the value(s) of where the tangent line is horizontal;, f(x) =x" (x - 10)3 {(= Select the correct choice below and; if necessary; fill in the answer box within your choice. 0 A The tangent line is horizontal at x = (Use comma t0 separate answers as needed 0 B: The tangent line is never horizontal;



Answers

Let $f(x)=x^{3}$ a. Find the point on the graph of $f$ where the tangent line is horizontal. b. Sketch the graph of $f$ and draw the horizontal tangent line.

Okay, well, given if Alexis, because X cubed plus X squared minus experts one and were asked to determine the points for which the slope of the tangent line is a horizontal. That's when at time of ecstasy deserved and then b F. When the slope of the tangent line isn't good ones, it's prime of X is equal to make it one. All right, let's stick to your job is equal to three x squared two X minus one. Looking in for setting the secret is oh Eaton's office. This is this three x minus One times X plus. One is bill till our points, when thanks are written with a slope of detention line is horizontal is when x you got the negative one and X is equal to one over three. Right now, when after that or when, the tangent line is a negative one, we have see me X squared minus plus two X minus one is equal to one one's canceled. We get X Three extras to you could you know that's extra vehicle to zero and exit people to negative to build victory

For this given exercise, we want to first look at our function F of X equals X squared plus three acts. Thanks kim. And then we want to find the slope of the tangent line at a general point X. Not so we're going to differentiate this and we know the F prime of X is going to end up equaling This is the power rule here, so we bring it to on front. So it's gonna be two X. Class here. This is just three acts. So we just take the contents of of two X plus three. And that's our final um That's going to be the derivative of the function when we let X not equal X. So now we want to find f crime of, It's not as equal to two. So we're going to find f prime of two, Liquidity is two times 2 plus three, which is four plus three. So that's seven as our final answer.

For the given exercise. What we want to do is start by looking at our function which is F of X equals the square root of axe. And then we want to evaluate this um at X zero equals one. Before we do that we want to take the derivative. So it's important that we look at X slightly differently. Let's view it as X to the one half. Because then we can use the power rule. Um and using the power roll we get that F prime of act is equal to one half, X to the negative one half. That's the same thing as 1/2 or one over to root X. So we could just write it like that over two X. So now that we have this, we want to evaluate it since this is X not we want to evaluate it at one. So it would be 1/2 times route one. Route one is one. So this is going to end up being one half as our final answer.

The problem giving here, we want to look at f of X equals X squared plus one, and we know the X not is equal to two. We want to find the slope of the tangent line at a general point X. Not. And then we want to use the result from part A to find the slope of the tangent line at the given value X. Not. So we have F of X equals X squared plus one. So F prime of X is going to end up equaling um X. R two x what's zero? So there's to actually be the answer for this and that's two X not. So in this case are ex not value is going to be two. So that tells us the F prime of chew is equal to two times 2, which equals four. That's gonna be our final answer.


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