EXAMPLE 5Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).SOLUTIONFrom the previous example, we know the derivative of f(x)x - 8x + 9 at the number a is fÂ '(a)= 2a - 8. Therefore the slope of the tangentyline at (1, 2) is fÂ '(1)= 2(1) - 8 =2Thus an equation of the tangent line, shown in the figure, is1y - ((x -or y =|x + 8

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Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.4: Solving Nonlinear Equations

Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...

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Question

EXAMPLE 5
Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).
SOLUTION
From the previous example, we know the derivative of f(x)
x - 8x + 9 at the number a is fÂ '(a)
= 2a - 8. Therefore the slope of the tangent
y
line at (1, 2) is fÂ '(1)
= 2(1) - 8 =
2
Thus an equation of the tangent line, shown in the figure, is
1
y - (
(x -
or y =
|x + 8

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