i only need help with parts b,d,h,and i In this question, you will sketch the gr

Question

i only need help with parts b,d,h,and i

In this question, you will sketch the graph of the cubic function below.

The derivative of this function can be shown to equal

This derivative can be factored as follows:

The second derivative of the function is given by

(a) At what two values of x does the derivative of f(x) equal zero?
(Enter the smaller solution in the first box and the larger solution in the second box.)
Smaller solution :
Larger solution :
(b) Which of the following descriptions apply to the function f(x)? (Check all that apply.)

(c) At what value of x does the second derivative of f(x) equal zero?
x :
(d) Which of the following descriptions apply to the function f(x)? (Check all that apply.)

(h) What is the y intercept of the function?
y intercept :
(i) Find the x intercepts of the function.
(Enter these numbers in order, from the smallest to the largest.)
Smallest x intercept :

Middle x intercept :

Largest x intercept :

In this question, you will sketch the graph of the cubic function below. f(x) = 2x3 + 12x2 - 270x The derivative of this function can be shown to equal f'(x) = 6x2 + 24x - 270 This derivative can be factored as follows: f'(x) = 6(x + 9)(x - 5) The second derivative of the function is given by f"(x) = 12x + 24 At what two values of x does the derivative of f(x) equal zero? Which of the following descriptions apply to the function f(x)? At what value of x does the second derivative of f(x) equal zero? Which of the following descriptions apply to the function f(x)? Find the x intercepts of the function.

Explanation / Answer

a) -9,5

b) decreasing in (-9,5)

increasing (-infinite,-9)

and in (5,infinite)

d) concave upwards in (-2, infinite)

concave downwards in (- infinite,-2)

h)

y intercept x=0

i) x intercept =0,9,-15

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