Question

The graph of a derivative f' is shown to the right. Use the information in the graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of f. Where is the function increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) A. The function f is increasing on and decreasing on . B. The function f is decreasing on and never increasing. C. The function f is increasing on and never decreasing.

          The graph of a derivative f' is shown to the right. Use the information in the graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of f.
Where is the function increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
(Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
A. The function f is increasing on and decreasing on .
B. The function f is decreasing on and never increasing.
C. The function f is increasing on and never decreasing.

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The graph of a derivative f' is shown to the right. Use the information in the graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of f.
Where is the function increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
(Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
A. The function f is increasing on and decreasing on .
B. The function f is decreasing on and never increasing.
C. The function f is increasing on and never decreasing.

Added by Jasmine C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert H M

05/22/2023

Step 1

From the given graph of the derivative, we can see that the derivative is positive when x is in the interval (a, b) and negative when x is in the interval (c, d). Show more…

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The graph of a derivative f' is shown to the right. Use the information in the graph to determine where f is increasing or decreasing and the x-values of any extrema. Then sketch a possible graph of f. Where is the function increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) A. The function f is increasing on and decreasing on . B. The function f is decreasing on and never increasing. C. The function f is increasing on and never decreasing.

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Transcript

00:01 We are given the graph of f prime.

00:03 We know that f is increasing where the derivative f prime is positive, so greater than zero.

00:14 So we see that f prime is positive here, so from negative infinity to negative three, the x values, and also here.

00:32 So that is from positive one to positive infinity.

00:40 And f is decreasing where f prime is negative, so less than zero.

00:51 I see that f prime is negative in this region, so that is from negative three to positive one.

01:06 Also, i should note that when you are entering your solutions, you will use a comma instead of a u.

01:15 Also, f will have extrema at f equals c, where f prime of c equals zero.

01:32 And f prime before c, so i'll call that less than c, has the opposite sign.

01:40 So i'll just write this as the sign of f prime of c is opposite the sign of f prime of after c.

01:53 Okay, so that's greater than c.

01:57 So i hope that's not too confusing.

01:59 I will show you this.

02:00 So we see that there is a point here, where f prime is zero.

02:07 And before that point, f prime is positive.

02:11 And after that point, f prime is negative.

02:14 So that means f prime changes sign at this point.

02:18 So there will be an extrema at this point, and it will be at x equals negative three.

02:26 There is also another point where f prime is zero, that is here.

02:32 Okay, we see that before that point, f prime is negative...

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