Question

(a) Find the critical points, if any, of the following function on the given interval. (b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither. (c) Find the absolute maximum and minimum values on the given interval. f(x) = (7 - x) / (x^2 - 4x - 5) ; [- 10,10] (a) Find the critical points, if any, of f(x) on [- 10,10]. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The critical point(s) is(are) x = 3. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) B. There are no critical points. (b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither. Identify all local maxima, if any, of f(x). Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is a local maximum at x = . (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) B. There are no local maxima.

          (a) Find the critical points, if any, of the following function on the given interval.
(b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither.
(c) Find the absolute maximum and minimum values on the given interval.
f(x) = (7 - x) / (x^2 - 4x - 5) ; [- 10,10]
(a) Find the critical points, if any, of f(x) on [- 10,10]. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The critical point(s) is(are) x = 3.
(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
B. There are no critical points.
(b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither. Identify all local maxima, if any, of f(x). Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. There is a local maximum at x = .
(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
B. There are no local maxima.

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(a) Find the critical points, if any, of the following function on the given interval.
(b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither.
(c) Find the absolute maximum and minimum values on the given interval.
f(x) = (7 - x) / (x^2 - 4x - 5) ; [- 10,10]
(a) Find the critical points, if any, of f(x) on [- 10,10]. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The critical point(s) is(are) x = 3.
(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
B. There are no critical points.
(b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither. Identify all local maxima, if any, of f(x). Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. There is a local maximum at x = .
(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
B. There are no local maxima.

Added by Christine A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

07/28/2023

Step 1

f'(x) = 2x - A Now, we need to find the critical points by setting the derivative equal to 0. 2x - A = 0 x = A/2 Since the interval is [-10, 10], we need to check if A/2 is within this interval. We don't have the value of A, so we can't find the exact Show more…

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(a) Find the critical points, if any, of the following function on the given interval. (b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither. (c) Find the absolute maximum and minimum values on the given interval. f(x) = (7 - x) / (x^2 - 4x - 5); [-10, 10] (a) Find the critical points, if any, of f(x) on [-10, 10]. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The critical point(s) is(are) x = 3. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) B. There are no critical points. (b) Use a graphing device to determine whether the critical points correspond to local maxima, local minima, or neither. Identify all local maxima, if any, of f(x). Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is a local maximum at x = . (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) B. There are no local maxima.

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Transcript

00:01 So what we have to do in this problem is factor the denominator.

00:07 So i'm looking at that x squared minus 4x minus 5.

00:10 I'm going to go ahead and rewrite it as x minus 5 and then x plus 1.

00:16 That should work for us.

00:19 And so as i'm, actually i probably should have left it the way it was, 7 minus x over what i say, x squared minus 4x minus 5.

00:29 Because if you're trying to find where we are increasing or decreasing, you'd want to know the derivative of that.

00:39 So a few things i do want to point out though is that x cannot equal 5 or negative 1.

00:44 That's kind of why i do that work.

00:47 So then we're going to do the derivative where the derivative of the top would be negative 1.

00:51 We leave the bottom alone.

00:55 And then minus the derivative of the bottom which is 2x minus 4.

01:00 Leave the top alone.

01:01 And then all over the denominator squared which is just reiterating that you have those domain restrictions.

01:11 But what i would do next is see where the numerator equals zero.

01:14 So i'm going to distribute that negative x plus 5.

01:19 And here i'm going to distribute, what do i end up with? a negative 2x squared and then a 14x with a 4x.

01:34 So that's 18x.

01:37 And then negative 4 times 7 should be negative 28...

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