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ACTIVITY 3: Estimating slope of a tangent line, limits of a function & One-sided limits Estimate the slope of a line tangent to the curve f(x) -2x² + 3x + 5 at point P(1, f(1))by doing the following step. Sketch the graph of f(x) and make a tangent line at point P. Label the graph and the tangent line. ii. A. i. Consider point Q(2.5, f(2.5)) along with the graph of f(x). Make a line connecting point P and point Q. Label the line by "Secant Line PQ". Find the slope mpg of the secant line PQ. iii. Let the point Q(x, f(x)) be the arbitrary point along the graph of f(x) where the value of x must be in between 1 and 2.5 (i.e. 1

ACTIVITY 3: Estimating slope of a tangent line, limits of a function & One-sided limits Estimate the slope of a line tangent to the curve f(x) -2x² + 3x + 5 at point P(1, f(1))by doing the following step. Sketch the graph of f(x) and make a tangent line at point P. Label the graph and the tangent line. ii. A. i. Consider point Q(2.5, f(2.5)) along with the graph of f(x). Make a line connecting point P and point Q. Label the line by "Secant Line PQ". Find the slope mpg of the secant line PQ. iii. Let the point Q(x, f(x)) be the arbitrary point along the graph of f(x) where the value of x must be in between 1 and 2.5 (i.e. 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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Answer part i and iii.
ACTIVITY 3: Estimating slope of a tangent line, limits of a function & One-sided limits · Estimate the slope of a line tangent to the curve f (x) = -2x? + 3x + 5 at point P(1, f(1))by doing the following step. Sketch the graph of f(x) and make a tangent line at point P. Label the graph and the tangent line. Consider point Q(2.5, f(2.5)) along with the graph of f(x). Make a line connecting point P and point Q. Label the line by "Secant Line PQ". Find the slope mpg of the secant line PQ. Let the point Q(x, ƒ(x)) be the arbitrary point along the graph of f(x) where the value of x must be in between 1 and 2.5 (i.e. 1< x < 2.5). Let P(x1,y1) = P(1, f(1)) and Q(x2, y2) = Q(x, f(x), find the expression of the slope mpQ- Note: The expression of the slope mpo is a function of x. (Hint: mpo(x) = *-Y1) A. i. ii. ii. X2-X1 iv. Give at least 5 values for x beginning from x = 2.5 that moves closer and closer to x = 1. Substitute these values to the expression of the slope mpQ(x). Make sure that your chosen x's can approximate the slope for the tangent line. Show your computation and make a table of values as shown below. (Round off the slope up to 6 decimal places) mpQ(x) 2.5 V. Determine the exact value of the slope of tangent line based on where the values of slope mpo is approaching as x approaches 1?
Transcribed Image Text:ACTIVITY 3: Estimating slope of a tangent line, limits of a function & One-sided limits · Estimate the slope of a line tangent to the curve f (x) = -2x? + 3x + 5 at point P(1, f(1))by doing the following step. Sketch the graph of f(x) and make a tangent line at point P. Label the graph and the tangent line. Consider point Q(2.5, f(2.5)) along with the graph of f(x). Make a line connecting point P and point Q. Label the line by "Secant Line PQ". Find the slope mpg of the secant line PQ. Let the point Q(x, ƒ(x)) be the arbitrary point along the graph of f(x) where the value of x must be in between 1 and 2.5 (i.e. 1< x < 2.5). Let P(x1,y1) = P(1, f(1)) and Q(x2, y2) = Q(x, f(x), find the expression of the slope mpQ- Note: The expression of the slope mpo is a function of x. (Hint: mpo(x) = *-Y1) A. i. ii. ii. X2-X1 iv. Give at least 5 values for x beginning from x = 2.5 that moves closer and closer to x = 1. Substitute these values to the expression of the slope mpQ(x). Make sure that your chosen x's can approximate the slope for the tangent line. Show your computation and make a table of values as shown below. (Round off the slope up to 6 decimal places) mpQ(x) 2.5 V. Determine the exact value of the slope of tangent line based on where the values of slope mpo is approaching as x approaches 1?
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