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1 COS 4 Now, differentiate f'(x) with respect to x. - 4 -x* sin(x4) f"(x) = -x°•si Submit Skip (you cannot come back).

1 COS 4 Now, differentiate f'(x) with respect to x. - 4 -x* sin(x4) f"(x) = -x°•si Submit Skip (you cannot come back).

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 point of inflection and discuss the concavity of the graph of the function. f(x) = sin 4' [0, 87] Step 1 Let f be a function whose second derivative exists on a closed open interval I. If f"(x) > 0 for all x in I, then the graph of f is concave upward upward on I. And if f"(x) < 0 for all x in I, then the graph of f is concave downward downward on I. If a tangent line exists at a point where concavity changes, this point is called a point of inflection. Step 2 If (c, f(c)) is a point of inflection of the graph of f, then either f"(c) = 0 or f" does not exist at x = c. Differentiate f(x) with respect to x. f'(x) COS %3D Step 3 Now, differentiate f'(x) 1 COS with respect to x. f"(x) = -x3. sin(x4) Submit Skip (you cannot come back)
Transcribed Image Text:Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin 4' [0, 87] Step 1 Let f be a function whose second derivative exists on a closed open interval I. If f"(x) > 0 for all x in I, then the graph of f is concave upward upward on I. And if f"(x) < 0 for all x in I, then the graph of f is concave downward downward on I. If a tangent line exists at a point where concavity changes, this point is called a point of inflection. Step 2 If (c, f(c)) is a point of inflection of the graph of f, then either f"(c) = 0 or f" does not exist at x = c. Differentiate f(x) with respect to x. f'(x) COS %3D Step 3 Now, differentiate f'(x) 1 COS with respect to x. f"(x) = -x3. sin(x4) Submit Skip (you cannot come back)
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