4. The twice-differentiable function f is defined for all real numbers and satisfies the following conditions: f(0) = -2, f'(0) = 3, f"(0) = -1. A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a constant. Find g'(0) and g"(0) in terms of a %3D B. The function h is given by h(x) = sin(kx) · f (x) for all real numbers, where k is a constant. Find h'(x) and write an equation for the line tangent to the graph of h at

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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4. The twice-differentiable function f is defined for all real numbers and satisfies the
following conditions: f(0) = -2, f'(0) = 3, f"(0) = -1.
A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a
constant. Find g'(0) and g"(0) in terms of a
%3D
B. The function h is given by h(x) = sin(kx) · f (x) for all real numbers, where k is a
constant. Find h'(x) and write an equation for the line tangent to the graph of h at
Transcribed Image Text:4. The twice-differentiable function f is defined for all real numbers and satisfies the following conditions: f(0) = -2, f'(0) = 3, f"(0) = -1. A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a constant. Find g'(0) and g"(0) in terms of a %3D B. The function h is given by h(x) = sin(kx) · f (x) for all real numbers, where k is a constant. Find h'(x) and write an equation for the line tangent to the graph of h at
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