Chapter 11.4, Problem 3E

Solution

To calculate: The numerical derivative of the function $f\left(x\right)=3x^2+2$ by graphing calculator at the specified point.

The numerical derivative of $f\left(x\right)=3x^2+2$ at the specified point $x=-2$ is $-12$ .

Given information: The given function is $f\left(x\right)=3x^2+2$ and the specified point is $x=-2$ .

Calculation:

To find the numerical derivative of the function $f\left(x\right)=3x^2+2$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{MATH}}$ key and select $\text{nDeriv(}$ under math. Enter the given function, variable $x$ and the given $x$ -value.

Press the $\boxed{\text{ENTER}}$ key to find the numerical derivative of the function as shown below in Figure (1).

  

Figure (1)

Thus, the numerical derivative of the given function is $-12$ .