Q. 9 - Calculus

Question

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).

Step-by-Step Solution

Answer

Graph is:

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.

Step 2. Sketch the graph

Since, $f^{\mathrm{\prime }}(-2)=0$ so $-2$ is a critical point.

and $f^{\text{'}}\left(1\right)$ oes not exist so it has extremum at 1.

also $f^{\text{'}}$ is positive only on (-2,1) so f is increasing in the interval (-2,1)

Thus, the Graph is: