Question

use a graphing calculator to graph a derivative of the function use the TRACE function to find the values of x for which the slope of the tangent line (Y) is positive, negative, and 0y=12-x^2

Answer 1

We basically have to find the places where the slope of tangent line is

negative, 0 , and positive.

That is, taking the derivative of the function and graphing that.

Wherever that is negative, 0 , and positive, that is our answer.

The function is:

$y=12-x^2$

Derivative is:

$y^{\prime}=-2x$

Graph of the function "2x" (line):

As u can see,

Positive

x < 0

Zero

at x = 0

Negative

x > 0