5. (3 points) for the function f, whose graph is shown below, determine the sign of each of the following…

5. (3 points) for the function f, whose graph is shown below, determine the sign of each of the following: positive, negative, or zero.\na. f(0)\nb. f(0)\nc. f(4)\nd. f(4)

5. (3 points) for the function f, whose graph is shown below, determine the sign of each of the following: positive, negative, or zero.\na. f(0)\nb. f(0)\nc. f(4)\nd. f(4)

Answer

Explanation:

Step1: Find f(0)

Look at x = 0 on the graph. The y - value at x = 0 is positive.

Step2: Find f'(0)

The slope of the tangent line to the graph of y = f(x) at x = 0 is zero since the function has a local maximum at x = 0.

Step3: Find f(4)

Look at x = 4 on the graph. The y - value at x = 4 is negative.

Step4: Find f'(4)

The slope of the tangent line to the graph of y = f(x) at x = 4 is positive as the function is increasing at x = 4.

Answer:

a. Positive b. Zero c. Negative d. Positive