Let f(x) = x¹ - 50x² 3 (a) Use the definition of a derivative or the derivative rules to find ƒ'(x) = (b) Use the definition of a derivative or the derivative rules to find f''(x) = (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = (e) On what interval is f concave downward (include the endpoints in the interval)? interval of concave downward = (f) On what interval is f concave upward (include the endpoints in the interval)? interval of concave upward

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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Let f(x)
=
x¹ - 50x²
3
(a) Use the definition of a derivative or the derivative rules to find
ƒ'(x) =
(b) Use the definition of a derivative or the derivative rules to find
f''(x)
=
(c) On what interval is f increasing (include the endpoints in the interval)?
interval of increasing =
(d) On what interval is f decreasing (include the endpoints in the interval)?
interval of decreasing =
(e) On what interval is f concave downward (include the endpoints in the interval)?
interval of concave downward =
(f) On what interval is f concave upward (include the endpoints in the interval)?
interval of concave upward
Transcribed Image Text:Let f(x) = x¹ - 50x² 3 (a) Use the definition of a derivative or the derivative rules to find ƒ'(x) = (b) Use the definition of a derivative or the derivative rules to find f''(x) = (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = (e) On what interval is f concave downward (include the endpoints in the interval)? interval of concave downward = (f) On what interval is f concave upward (include the endpoints in the interval)? interval of concave upward
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ISBN:
9780321964038
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