The derivative of a polynomial function, f(x), is represented by the equation f'(x) = -2x(x – 3)^2. Additionally, f(1) = -3. Use this information to answer the following questions.

PART A: On what interval(s) is the graph of f(x) increasing? Decreasing? Justify your reasoning.
PART B: At what value(s) of x does the graph of f(x)have relative maximum? A relative minimum?
Justify your reasoning.
PART C What is the equation of the tangent line to f at x = 1?

the correct answer is 828.07

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

b is the correct answer