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The point P(4, -2) lies on the curve y = -

The point P(4, -2) lies on the curve y = -

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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The point P(4, -2) lies on the curve y = 3 - x (a) If Q is the point x, ), find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (i) 3.9 (i1) 3.99 mpg (ii) 3.999 (iv) 3.9999 (v) 4.1 (vi) 4.01 mpo = (vii) 4.001. (viii) 4.0001 mpo = (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(4, -2). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2). Need Help? Read It
Transcribed Image Text:The point P(4, -2) lies on the curve y = 3 - x (a) If Q is the point x, ), find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (i) 3.9 (i1) 3.99 mpg (ii) 3.999 (iv) 3.9999 (v) 4.1 (vi) 4.01 mpo = (vii) 4.001. (viii) 4.0001 mpo = (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(4, -2). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(4, -2). Need Help? Read It
A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) 20 25 30 5 10 15 V (gal) 2,064 1,329 765 339 87 (a) If P is the point (15, 765) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25, and 30. (Round your answers to one decimal place.) Slope (5, 2,064) (10, 1,329) | (20, 339) (25, 87) (30, 0) (b) Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P. (Round your answer to one decimal place.) Need Help? Master it Read It Watch it
Transcribed Image Text:A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) 20 25 30 5 10 15 V (gal) 2,064 1,329 765 339 87 (a) If P is the point (15, 765) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25, and 30. (Round your answers to one decimal place.) Slope (5, 2,064) (10, 1,329) | (20, 339) (25, 87) (30, 0) (b) Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P. (Round your answer to one decimal place.) Need Help? Master it Read It Watch it
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