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SECTION 2.7 DERIVATIVES AND RATES OF CHANGE 151 22. Sketch the graph of a function g for which g(0) = g(2) = g(4) = 0, g'(1) = g'(3) = 0, g'(0) = g'(4) = 1, %3D g'(2) = = -∞. -1, lim,. g(x) = 0, and lim,- g(x) 23. If f(x) = 3x² – x³, find f'(1) and use it to find an equation of the tangent line to the curve y 6. 3x2 - x' at the point (1, 2). %3D 24. If g(x) = x* - 2, find g'(1) and use it to find an equation of the tangent line to the curve y = x* - 2 at the point (1, -1). 25. (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an %3D equation of the tangent line to the curve y = 5x/(1 + x²) at the point (2, 2). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. 26. (a) If G(x) = 4x² – x', find G'(a) and use it to find equations of the tangent lines to the curve y = 4x2 - x' at the points (2,8) and (3, 9).

SECTION 2.7 DERIVATIVES AND RATES OF CHANGE 151 22. Sketch the graph of a function g for which g(0) = g(2) = g(4) = 0, g'(1) = g'(3) = 0, g'(0) = g'(4) = 1, %3D g'(2) = = -∞. -1, lim,. g(x) = 0, and lim,- g(x) 23. If f(x) = 3x² – x³, find f'(1) and use it to find an equation of the tangent line to the curve y 6. 3x2 - x' at the point (1, 2). %3D 24. If g(x) = x* - 2, find g'(1) and use it to find an equation of the tangent line to the curve y = x* - 2 at the point (1, -1). 25. (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an %3D equation of the tangent line to the curve y = 5x/(1 + x²) at the point (2, 2). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. 26. (a) If G(x) = 4x² – x', find G'(a) and use it to find equations of the tangent lines to the curve y = 4x2 - x' at the points (2,8) and (3, 9).

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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SECTION 2.7 DERIVATIVES AND RATES OF CHANGE 151 22. Sketch the graph of a function g for which g(0) = g(2) = g(4) = 0, g'(1) = g'(3) = 0, g'(0) = g'(4) = 1, %3D g'(2) = = -∞. -1, lim,. g(x) = 0, and lim,- g(x) 23. If f(x) = 3x² – x³, find f'(1) and use it to find an equation of the tangent line to the curve y 6. 3x2 - x' at the point (1, 2). %3D 24. If g(x) = x* - 2, find g'(1) and use it to find an equation of the tangent line to the curve y = x* - 2 at the point (1, -1). 25. (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an %3D equation of the tangent line to the curve y = 5x/(1 + x²) at the point (2, 2). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. 26. (a) If G(x) = 4x² – x', find G'(a) and use it to find equations of the tangent lines to the curve y = 4x2 - x' at the points (2,8) and (3, 9).
Transcribed Image Text:SECTION 2.7 DERIVATIVES AND RATES OF CHANGE 151 22. Sketch the graph of a function g for which g(0) = g(2) = g(4) = 0, g'(1) = g'(3) = 0, g'(0) = g'(4) = 1, %3D g'(2) = = -∞. -1, lim,. g(x) = 0, and lim,- g(x) 23. If f(x) = 3x² – x³, find f'(1) and use it to find an equation of the tangent line to the curve y 6. 3x2 - x' at the point (1, 2). %3D 24. If g(x) = x* - 2, find g'(1) and use it to find an equation of the tangent line to the curve y = x* - 2 at the point (1, -1). 25. (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an %3D equation of the tangent line to the curve y = 5x/(1 + x²) at the point (2, 2). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. 26. (a) If G(x) = 4x² – x', find G'(a) and use it to find equations of the tangent lines to the curve y = 4x2 - x' at the points (2,8) and (3, 9).
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