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1. This question concerns the function y = f(x) = 2 - 3x² near the point where x = 1. (a) What is f(1)? (b) Write in terms of h the slope of the secant line through the points (1, f(1)) and (1+h, ƒ(1+h)). Simplify. (Use algebra, but take no limits yet.) (c) Use your answer to (b) to find the slope of the tangent line to y = f(x) at x = 1.

1. This question concerns the function y = f(x) = 2 - 3x² near the point where x = 1. (a) What is f(1)? (b) Write in terms of h the slope of the secant line through the points (1, f(1)) and (1+h, ƒ(1+h)). Simplify. (Use algebra, but take no limits yet.) (c) Use your answer to (b) to find the slope of the tangent line to y = f(x) at x = 1.

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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Can you answer 1c?

1. This question concerns the function y = f(x) = 2 - 3x² near the point where x = 1. (a) What is f(1)? (b) Write in terms of h the slope of the secant line through the points (1, ƒ(1)) and (1+h, ƒ(1+h)). Simplify. (Use algebra, but take no limits yet.) (c) Use your answer to (b) to find the slope of the tangent line to y = f(x) at x = 1. (d) Use your answer to (c) to write an equation of the tangent line to y = f(x) at x = 1. (It need not be in slope-intercept form.)
Transcribed Image Text:1. This question concerns the function y = f(x) = 2 - 3x² near the point where x = 1. (a) What is f(1)? (b) Write in terms of h the slope of the secant line through the points (1, ƒ(1)) and (1+h, ƒ(1+h)). Simplify. (Use algebra, but take no limits yet.) (c) Use your answer to (b) to find the slope of the tangent line to y = f(x) at x = 1. (d) Use your answer to (c) to write an equation of the tangent line to y = f(x) at x = 1. (It need not be in slope-intercept form.)
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