f(x)= 2x^3 + 12x^2 -270x The derivative of this function can be shown to equal f'(x)= 6x^2 +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 (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 th
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.)
(e) What are the co-ordinates of the
( , )
(f) What are the co-ordinates of the relative minimum point?
( , )
(g) What are the co-ordinates of the inflection point?
( , )
(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 :
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(e) What are the co-ordinates of the
( , )
(f) What are the co-ordinates of the relative minimum point?
( , )
(g) What are the co-ordinates of the inflection point?
( , )
(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 :
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