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Chapter 3: Q. 24 (page 261)

Find the possibility graph of its derivative f'.

Short Answer

Expert verified


The possibility graph of its derivative f' is

Step by step solution

01

Step 1. Given

The given information is

02

Step 2. Calculation

From the above graph, f'>0 at (- ∞, - 1) and (2, ∞) ; the function is increasing from (- ∞, - 1) and (2, ∞) ; the graph f' <0 at (-1,2) where the function is decreasing.

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Most popular questions from this chapter

Restate Theorem 3.3 so that its conclusion has to do with

tangent lines.

Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=x3−2x+1,[a,b]=[0,6]

For the graph of f in the given figure , approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points .

Last night at 6 p.m., Linda got up from her blue easy chair. She did not return to her easy chair until she sat down again at 8 p.m. Let s(t) be the distance between Linda and her easy chair t minutes after 6 p.m. last night.

(a) Sketch a possible graph of s(t), and describe what Linda did between 6 p.m. and 8 p.m. according to your graph. (Questions to think about: Will Linda necessarily move in a continuous and differentiable way? What are good ranges for t and s?

(b) Use Rolle’s Theorem to show that at some point between 6 p.m. and 8 p.m., Linda’s velocity v(t) with respect to the easy chair was zero. Find such a place on the graph of s(t).

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=x2(x-1)(x+1)
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