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Let f(x) = x^4 − 4x^3 − 20  (a) Find the first derivative f'(x) and the second derivative f"(x)  (b) Use f'(x) to find all critical points of f (c) Find the global maximum and global minimum of f on the interval where x is between −2 and 4. Give both the maximum value of f(x) and the x-value(s) where it is attained.

Let f(x) = x^4 − 4x^3 − 20  (a) Find the first derivative f'(x) and the second derivative f"(x)  (b) Use f'(x) to find all critical points of f (c) Find the global maximum and global minimum of f on the interval where x is between −2 and 4. Give both the maximum value of f(x) and the x-value(s) where it is attained.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
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 Let f(x) = x^4 − 4x^3 − 20

 (a) Find the first derivative f'(x) and the second derivative f"(x)

 (b) Use f'(x) to find all critical points of f

(c) Find the global maximum and global minimum of f on the interval where x is
between −2 and 4. Give both the maximum value of f(x) and the x-value(s) where it is attained. 

(d) Find the zeros of f"(x). Then decide which of these are inflection points. Hint: consider the sign of f" on either side of each zero of f"

 (d) Sketch the graph y=x^4-4x^3-20 labeling the global maximum and global minimum on {-2,4}, as well as any inflection points. 

Need help with both parts of (d)

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