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Chapter 3: Q. 9 (page 260)

Sketch the graph of a function f with the following properties:

f is continuous and defined on R;

f(0) = 5;

f(鈭�2) = 鈭�3 and f '(鈭�2) = 0;

f '(1) does not exist;

f' is positive only on (鈭�2, 1).

Short Answer

Expert verified

Graph is:

Step by step solution

01

Step 1. Given information

We have been given the following properties of a function f:

f is continuous and defined on R;

f(0) = 5;

f(鈭�2) = 鈭�3 and f '(鈭�2) = 0;

f '(1) does not exist;

f' is positive only on (鈭�2, 1)

We have to sketch the graph of this function.

02

Step 2. Sketch the graph

Since, f鈥�(鈭�2)=0so -2is a critical point.

and f'(1)oes not exist so it has extremum at 1.

also f'is positive only on (-2,1) so f is increasing in the interval (-2,1)

Thus, the Graph is:

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Most popular questions from this chapter

Given the following graph of f , graphically estimate the global extrema of f on each of the six intervals listed:

(a)-1,1(b)[2,鈭�)(c)[-2,1)(d)[0,2](e)(1,鈭�)(f)-鈭�,鈭�

Use Rolle鈥檚 Theorem to prove that if fis continuous and differentiable everywhere and has three roots, then its derivative f has at least two roots.

For Exercises 15鈥�20, sketch the graph of a function f that has the indicated characteristics. If a graph is not possible, explain why.

f negative, f' positive, and f'' positive on [0,3].

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Determine whether or not each function f in Exercises 41鈥�48 satisfies the hypotheses of Rolle鈥檚 Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c 鈭� (a, b) that satisfy the conclusion of Rolle鈥檚 Theorem.

fx=lnx2-1,a,b=-2,2
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