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3. Let f(x)= 3 cos x-4sin x+5 a) Determine the exact slope of f(x) at a: 4 %3D Зл b) Determine the tangent line approximation to y= f(x) at the point where a = 2 c) At the point where a = , is f(x) increasing, decreasing, or neither? Why?

3. Let f(x)= 3 cos x-4sin x+5 a) Determine the exact slope of f(x) at a: 4 %3D Зл b) Determine the tangent line approximation to y= f(x) at the point where a = 2 c) At the point where a = , is f(x) increasing, decreasing, or neither? Why?

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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Only need help on part 3 a,b,c
1. Consider the graph of the function y = p(x) that is provided below. Assume that each portion of the graph of p is a straight line, as pictured. a) State all values of a for which lim p(x) does not exist. 3. x>a b) State all values of a for which p is not continuous at a. -3 c) State all values of a for which p is not differentiable at x = a. d) On the axis provided (or on your own paper), sketch an accurate graph of y = p'(x) 2. Let fand g be differentiable functions for which of the following information is known: 4 1 f(2) = 5, g(2)=-2, f'(2) = g'(2) = -. 5 a) Let h be the new function defined by the rule h(x) = 3 f(x)-2g(x). Determine h(2) and h'(2) . b) Find an equation for the tangent line to y = h(x) at the point (2,h(2)). 1 c) Let p be the function defined by the rule p(x) = 2 f(x)+÷g(x). Is p increasing, decreasing, or neither at a = 2? Why? d) Estimate the value of p(2.05) by using the local linearization of p at the point (2, p(2)). 3. Let f(x)= 3 cos x-4sin x+5 a) Determine the exact slope of f(x) at a = 4 b) Determine the tangent line approximation to y = f(x) at the point where a = c) At the point where a = , is f(x) increasing, decreasing, or neither? Why?
Transcribed Image Text:1. Consider the graph of the function y = p(x) that is provided below. Assume that each portion of the graph of p is a straight line, as pictured. a) State all values of a for which lim p(x) does not exist. 3. x>a b) State all values of a for which p is not continuous at a. -3 c) State all values of a for which p is not differentiable at x = a. d) On the axis provided (or on your own paper), sketch an accurate graph of y = p'(x) 2. Let fand g be differentiable functions for which of the following information is known: 4 1 f(2) = 5, g(2)=-2, f'(2) = g'(2) = -. 5 a) Let h be the new function defined by the rule h(x) = 3 f(x)-2g(x). Determine h(2) and h'(2) . b) Find an equation for the tangent line to y = h(x) at the point (2,h(2)). 1 c) Let p be the function defined by the rule p(x) = 2 f(x)+÷g(x). Is p increasing, decreasing, or neither at a = 2? Why? d) Estimate the value of p(2.05) by using the local linearization of p at the point (2, p(2)). 3. Let f(x)= 3 cos x-4sin x+5 a) Determine the exact slope of f(x) at a = 4 b) Determine the tangent line approximation to y = f(x) at the point where a = c) At the point where a = , is f(x) increasing, decreasing, or neither? Why?
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