ƒ" (x) = x(x − 1)²(x + 2)³g" (x) = x(x − 1)²(x + 2)³ + 1h" (x) = x(x − 1)²(x + 2)³ - 1The twice-differentiable functions f, g, and h have second derivatives given above. Which of the functions f, g, and h have a graph with exactly two points of inflection?ABDg onlyhonlyfand g onlyf, g, and h12

For any function R(x), At its inflection point, R''(x) = 0 Therefore, at the inflection points of…

Answered: f" (x)= x(x-1)²(x + 2)³ g" (x) = x(x -…

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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The graph of y = f(x) has f(5) = -3 and f'(5) y = f(x)? = -3. Which of the following might be a graph of a None of these.
If f(x) = 3x² - x³, find f'(x), ƒ''(x), ƒ'''(x), and f(4)(x). f'(x) = f"(x) = f'(x) = f(4) (x) = Graph f, f', f", and f"" on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives? The graphs ---Select--- consistent with the geometric interpretations of the derivatives because f' ---Select--- --Select--- ✓where f' has a slope of m = 0, and f"" is ---Select--- ✓function equal to the slope of f". ✓where f has a slope of m = 0, f"
Use the graph of f and g. p(x) = f(x)g(x) g(x) = f(x) g(x) -2 10- 8 6 2 0 (a) Find p'(8). p'(8) = (b) Find q'(1). q'(1) = 2 4 X f 8 g 10
The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)
Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x7 1 g(x) 5х + 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.) (f(g(x)))' = (g(f(x)))' =
16-17. Find the derivative: y = (x² – 4x + 2)(2x3 - x2 +4) A) 2x* - 36x3 +24x2 + 4x -1 B) 2x* – 32x3 + 24x2 + 4x – 16 C) 10x* – 32x3 + 24x2 + 4x – 16 D) 10x-36x3 + 24x2 + 4x 16 | 18-19. Find using product rule y = x³ In x A) x? + 3x2 In x B) 3x2Inx C) x2 D) 3x

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