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x f(x) f'(x) g(x) g'(x) 1 1 1 3 3 4 3 65 1 3 -2 3 4 4-2 -6 51 6 The functions f and g have continuous derivatives. The table gives values of f, f', g, and g' at selected values of x. Part A: Find h'(3) if h(x) = g(f(x)). Part B: Find m' (2) if m(x) = f(x²). Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 6. Part D: Let j(x)= g(x) f(x) Find j'(4).

x f(x) f'(x) g(x) g'(x) 1 1 1 3 3 4 3 65 1 3 -2 3 4 4-2 -6 51 6 The functions f and g have continuous derivatives. The table gives values of f, f', g, and g' at selected values of x. Part A: Find h'(3) if h(x) = g(f(x)). Part B: Find m' (2) if m(x) = f(x²). Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 6. Part D: Let j(x)= g(x) f(x) Find j'(4).

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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x_f(x) f'(x) g(x) g'(x) 34 1 6 1 1 3 3 4 1 3 4-2 -6 5 1 6 5 3 Part D: Let j(x)= -2 The functions f and g have continuous derivatives. The table gives values of f, f', g, and g' at selected values of x. Part A: Find h'(3) if h(x) = g(f(x)). Part B: Find m' (2) if m(x) = f(x²). Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 6. g(x) f(x) Find j'(4).
Transcribed Image Text:x_f(x) f'(x) g(x) g'(x) 34 1 6 1 1 3 3 4 1 3 4-2 -6 5 1 6 5 3 Part D: Let j(x)= -2 The functions f and g have continuous derivatives. The table gives values of f, f', g, and g' at selected values of x. Part A: Find h'(3) if h(x) = g(f(x)). Part B: Find m' (2) if m(x) = f(x²). Part C: Let k(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 6. g(x) f(x) Find j'(4).
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