Question

1. The graph of the derivative, y = f'(x), of the continuous function, y = f(x), is shown below. (a) On what interval(s) is the function f increasing or decreasing? (b) At what values of x does f have a local maximum or local minimum? (c) On what interval(s) is the function f concave up? concave down? (d) State the x- coordinates of the point(s) of inflection of f.

          1. The graph of the derivative, y = f'(x), of the continuous function, y = f(x), is shown below.
(a) On what interval(s) is the function f increasing or decreasing?
(b) At what values of x does f have a local maximum or local minimum?
(c) On what interval(s) is the function f concave up? concave down?
(d) State the x- coordinates of the point(s) of inflection of f.

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1. The graph of the derivative, y = f'(x), of the continuous function, y = f(x), is shown below.
(a) On what interval(s) is the function f increasing or decreasing?
(b) At what values of x does f have a local maximum or local minimum?
(c) On what interval(s) is the function f concave up? concave down?
(d) State the x- coordinates of the point(s) of inflection of f.

Added by Joy C.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Gregory Higby

04/13/2023

Step 1

The function is increasing where the derivative is positive and decreasing where the derivative is negative. From the graph, we can see that the derivative is positive on the intervals $(-\infty, -2)$ and $(1, \infty)$, and negative on the interval $(-2, 1)$. So, Show more…

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1. The graph of the derivative, y = f'(x), of the continuous function, y = f(x), is shown below. (a) On what interval(s) is the function f increasing or decreasing? (b) At what values of x does f have a local maximum or local minimum? (c) On what interval(s) is the function f concave up? concave down? (d) State the x- coordinates of the point(s) of inflection of f.

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Transcript

00:01 So you definitely need to be careful on a problem like this because they're giving you the graph of the derivative.

00:07 So i'm going to point out negative 2, negative 1, 1, and 3.

00:14 I think those are the only points i really need to know.

00:17 Well, 4 i also need to know.

00:20 So if i'm reading this correctly, we have a max.

00:23 We have a 0, an arrow down.

00:26 We have a minimum and a 0 at 1.

00:29 And then an open circle, and then another open circle, and then another 0 at 4 with an open circle at 5.

00:41 I guess i should clarify that as well.

00:43 So if f is increasing, that's because f prime is positive.

00:53 Double -edded arrow.

00:55 So we can answer this question on the interval from negative 2 to 1.

01:01 I'm going to put a little break there because it's actually equal 0 at 1.

01:07 And then 1 to 3, where 3 is undefined.

01:11 And then from 3 to 4.

01:15 So if i flip that around, where is f decreasing? so again, a double -headed arrow here.

01:23 F prime would be negative.

01:25 And that interval would be, well, the arrowhead would be from negative infinity to negative 3, excuse me, negative 2, as well as 4 to 5 because it's an open circle at 5...

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