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(a) Find the slope of the tangent line to the parabola y = x² + 6x at the point (-2, -8) by using the following parameters. (0) The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m = lim f(x)-f(a) provided that this limit exists. 1 - ਬ (ii) The expression of slope is m lim f(a+h)-f(a) h - h m= y = (b) Find an equation of the tangent line in part (a). m = 0 (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-2, -8) until the parabola and the tangent line are indistinguishable. y -10 -5 y 20 10 -10 -20 10 -10 -5 20₁ 10 -10 -20 5 10 -10 10 -10 -10 -105 0

(a) Find the slope of the tangent line to the parabola y = x² + 6x at the point (-2, -8) by using the following parameters. (0) The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m = lim f(x)-f(a) provided that this limit exists. 1 - ਬ (ii) The expression of slope is m lim f(a+h)-f(a) h - h m= y = (b) Find an equation of the tangent line in part (a). m = 0 (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-2, -8) until the parabola and the tangent line are indistinguishable. y -10 -5 y 20 10 -10 -20 10 -10 -5 20₁ 10 -10 -20 5 10 -10 10 -10 -10 -105 0

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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(a) Find the slope of the tangent line to the parabola y = x² + 6x at the point (-2, -8) by using the following parameters. f(x) = f(a) x-a (i) The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m = lim x→a m = (ii) The expression of slope is m = lim h→0 y = m = f(a+h)-f(a) h (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-2, -8) until the parabola and the tangent line are indistinguishable. y y y 201 20r 10 10 10 10 5 5 A A V V -10 -5 5 -10 -5 -5 5 -10 -10 -10 5 - 20 - 20 -10 -10 10 5 10 provided that this limit exists. X -10 X 5 X i
Transcribed Image Text:(a) Find the slope of the tangent line to the parabola y = x² + 6x at the point (-2, -8) by using the following parameters. f(x) = f(a) x-a (i) The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m = lim x→a m = (ii) The expression of slope is m = lim h→0 y = m = f(a+h)-f(a) h (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-2, -8) until the parabola and the tangent line are indistinguishable. y y y 201 20r 10 10 10 10 5 5 A A V V -10 -5 5 -10 -5 -5 5 -10 -10 -10 5 - 20 - 20 -10 -10 10 5 10 provided that this limit exists. X -10 X 5 X i
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