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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(−2) = −3 and f '(−2) = 0;

f '(1) does not exist;

f' is positive only on (−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(−2) = −3 and f '(−2) = 0;

f '(1) does not exist;

f' is positive only on (−2, 1)

We have to sketch the graph of this function.

02

Step 2. Sketch the graph

Since, f′(−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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