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Consider the graph of the function f (x) = x² – x – 72. (a) Find the equation of the secant line joining the points (–7, –16), and (9, 0). (b) Use the Mean Value Theorem to determine a point c in the interval (-7, 9) such that the tangent line at c is parallel to the secant line. (c) Find the equation of the tangent line through c. (d) Use a graphing utility to graph f, the secant line, and the tangent line. 20 y 40 -20 60 40 -20 20 60 10 20 y 20 y 40 -20 20 40 60 40 -20 20 60

Consider the graph of the function f (x) = x² – x – 72. (a) Find the equation of the secant line joining the points (–7, –16), and (9, 0). (b) Use the Mean Value Theorem to determine a point c in the interval (-7, 9) such that the tangent line at c is parallel to the secant line. (c) Find the equation of the tangent line through c. (d) Use a graphing utility to graph f, the secant line, and the tangent line. 20 y 40 -20 60 40 -20 20 60 10 20 y 20 y 40 -20 20 40 60 40 -20 20 60

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Consider the graph of the function f (x) = x2 – x – 72. (a) Find the equation of the secant line joining the points (-7, -16), and (9, 0). (b) Use the Mean Value Theorem to determine a point c in the interval (-7, 9) such that the tangent line at c is parallel to the secant line. C = (c) Find the equation of the tangent line through c. (d) Use a graphing utility to graph f, the secant line, and the tangent line. 20 y 20 y -60 -40 -20 20 40 60 -60 -40 -20 20 40 60 To -80 20 y 20 y -40 -20 20 40 60 -60 -40 -20 20 40 60 -60 -60 -80
Transcribed Image Text:Consider the graph of the function f (x) = x2 – x – 72. (a) Find the equation of the secant line joining the points (-7, -16), and (9, 0). (b) Use the Mean Value Theorem to determine a point c in the interval (-7, 9) such that the tangent line at c is parallel to the secant line. C = (c) Find the equation of the tangent line through c. (d) Use a graphing utility to graph f, the secant line, and the tangent line. 20 y 20 y -60 -40 -20 20 40 60 -60 -40 -20 20 40 60 To -80 20 y 20 y -40 -20 20 40 60 -60 -40 -20 20 40 60 -60 -60 -80
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