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Define H(a) = ln(1 +1²)dt. Compute H'(x), H"(x), and deduce the intervals of increase or decrease of H, its local extrema (if any), and the intervals where it is concave up or concave down. -x2

Define H(a) = ln(1 +1²)dt. Compute H'(x), H"(x), and deduce the intervals of increase or decrease of H, its local extrema (if any), and the intervals where it is concave up or concave down. -x2

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.
Chapter3: The Derivative
Section3.3: Rates Of Change
Problem 30E: If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing...
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Define 22 H(a) = ²² -x2 In(1 + t²)dt. Compute H'(x), H'(x), and deduce the intervals of increase or decrease of H, its local extrema (if any), and the intervals where it is concave up or concave down.
Transcribed Image Text:Define 22 H(a) = ²² -x2 In(1 + t²)dt. Compute H'(x), H'(x), and deduce the intervals of increase or decrease of H, its local extrema (if any), and the intervals where it is concave up or concave down.
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