x f(x) f'(x) g(x) g'(x) 34 1 6 1 4 -2 -6 1 3 5 1 3 3 6 5 1 3 -2 4 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) Part D: Let j(x)= Find /(4).
x f(x) f'(x) g(x) g'(x) 34 1 6 1 4 -2 -6 1 3 5 1 3 3 6 5 1 3 -2 4 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) Part D: Let j(x)= Find /(4).
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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Transcribed Image Text:x f(x) f'(x) g(x) g'(x)
3 4
1
6
1
4 -2 -6
1
3
5 1
3
6 5 1
3 -2
3
4
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: Letk(x) = f(g(x)). Write an equation for the line tangent to the graph of kat x = 6.
g(x)
f(x)
Part D: Let j(x)=
Find /'(4).
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