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Given: g(x) = -2x² + 3. Determine the slope of the secant lines the curve, given the coordinates P(1, 1), R(4, -29), S(3, -15), T(1.1, 0.58). PR, PS, and PT to

Given: g(x) = -2x² + 3. Determine the slope of the secant lines the curve, given the coordinates P(1, 1), R(4, -29), S(3, -15), T(1.1, 0.58). PR, PS, and PT to

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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1. Given: g(x) = -2x² + 3. Determine the slope of the secant lines the curve, given the coordinates P(1, 1), R(4, -29), S(3, -15), T(1.1, 0.58). PR, PS, and PT to 2. Using the value from number 1, describe what is happening to the value of the slope of the secant line from a point (x, y) as the point approaches P. 3. Estimate the slope of the tangent line at point, P. 4. Determine the derivative of g(x)=-2x² + 3 at x = 1, using the limit definition of the g(1+h)-g(1) derivative and the difference quotient, g'(1)=lim h-0 h 5. Determine the equation of the tangent line to g(x)= -2x² + 3 at x = 1.
Transcribed Image Text:1. Given: g(x) = -2x² + 3. Determine the slope of the secant lines the curve, given the coordinates P(1, 1), R(4, -29), S(3, -15), T(1.1, 0.58). PR, PS, and PT to 2. Using the value from number 1, describe what is happening to the value of the slope of the secant line from a point (x, y) as the point approaches P. 3. Estimate the slope of the tangent line at point, P. 4. Determine the derivative of g(x)=-2x² + 3 at x = 1, using the limit definition of the g(1+h)-g(1) derivative and the difference quotient, g'(1)=lim h-0 h 5. Determine the equation of the tangent line to g(x)= -2x² + 3 at x = 1.
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