Chapter 12.3, Problem 80E

To determine

To sketch: the graph of a function whose derivative is always negative.

Explanation of Solution

A function whose derivative is always positive is only possible if function has a degree of polynomial is 1 and the coefficient of variable is negative. So, here the function may be a linear function. But the graph of the function will vary, if there constant was vary.

Let the function will be

  $f\left(x\right)=-2x+3$

To graph of the function use graphing utility use TI-83 calculator:

For this open the TI-83 calculator and press the $Y=$ button and enter the function in the form of $x,y$ as:

  

Now press the window button and change the scale as choice.

  

Now press the graph button and it will show the graph as:

  

This is the graph of the derivative of function $f$ .

So, this is the graph of a function whose derivative is always negative.