N 2 -3 EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²-8x + 9 at the point (2, -3). SOLUTION From the previous example, we know the derivative of f(x)=x² - 8x + 9 at the number a is f'(a) = 2a - 8. Therefore the slope of the tangent line at (2, -3) is f'(2) = 2(2) - 8 = . Thus an equation of the tangent line, shown in the figure, is y- y = or -4x + 5
N 2 -3 EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²-8x + 9 at the point (2, -3). SOLUTION From the previous example, we know the derivative of f(x)=x² - 8x + 9 at the number a is f'(a) = 2a - 8. Therefore the slope of the tangent line at (2, -3) is f'(2) = 2(2) - 8 = . Thus an equation of the tangent line, shown in the figure, is y- y = or -4x + 5
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Question
Transcribed Image Text:N
2
-3
EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²-8x + 9 at the point
(2, -3).
SOLUTION From the previous example, we know the derivative of f(x)=x² - 8x + 9 at the
number a is f'(a) = 2a - 8. Therefore the slope of the tangent line at (2, -3) is
f'(2) = 2(2) - 8 =
. Thus an equation of the tangent line, shown in the figure, is
y-
y =
or
-4x + 5
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