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

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

6th Edition

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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