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Find the interval where the function is concave up. Find the interval where the function is concave down. Step 1 -8x Since f'(x) then %3D (x² – 4)2'

Find the interval where the function is concave up. Find the interval where the function is concave down. Step 1 -8x Since f'(x) then %3D (x² – 4)2'

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the interval where the function is concave up. Find the interval where the function is concave down. Step 1 -8x Since f'(x) = then (x2 4)2' (x² . 4)?(-8 - (-8x) 2(x² – 4)(2 f"(x) 4 (x² - 4) 8 3 3 x2 + 3 (x² 4) Step 2 The numerator is always positive, so the denominator determines the sign of f"(x). Thus, f"(x) is positive, and so f(x) is concave ---Select--- v, if x2 > conclude that f"(x) is negative, and so f(x) is concave ---Select--- ♥ which means x > or x < We can also if < X < Therefore the interval where the function is concave up is as follows. (Enter your answer using interval notation.) The interval where the function is concave down is as follows. (Enter your answer using interval notation.)
Transcribed Image Text:Find the interval where the function is concave up. Find the interval where the function is concave down. Step 1 -8x Since f'(x) = then (x2 4)2' (x² . 4)?(-8 - (-8x) 2(x² – 4)(2 f"(x) 4 (x² - 4) 8 3 3 x2 + 3 (x² 4) Step 2 The numerator is always positive, so the denominator determines the sign of f"(x). Thus, f"(x) is positive, and so f(x) is concave ---Select--- v, if x2 > conclude that f"(x) is negative, and so f(x) is concave ---Select--- ♥ which means x > or x < We can also if < X < Therefore the interval where the function is concave up is as follows. (Enter your answer using interval notation.) The interval where the function is concave down is as follows. (Enter your answer using interval notation.)
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