(a) Find the slope of the curve y=x²-3x-2 at the point P(2,-4) by finding the limit of the secant slopes through point P.(b) Find an equation of the tangent line to the curve at P(2,-4).(a) The slope of the curve at P(2,-4) is. (Simplify your answer.)(b) The equation of the tangent line to the curve at P(2,-4) is y=.***Time Remaining: 00:49:4

Answered: Image /qna-images/answer/3ca9a93e-712c-46c2-a06e-ecf763b12cd9.jpg

Answered: (b) Find an equation of the tangent…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 3E

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Find an equation of the tangent line to the parabola y = x2 - 6x + 7 at the point (2, -1). SOLUTION From the previous example, we know the derivative of f(x) = x2 - 6x + 7 at the number a is f '(a) = 2a - 6. Therefore the slope of the tangent line at (2, -1) is f '(2) = 2(2) - 6 = . Thus an equation of the tangent line, shown in the figure, is y - ( ) = (x - )or y = x + 3
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(b) Find an equation of the tangent line to the curve at P(2,-4). (a) The slope of the curve at P(2,-4) is. (Simplify your answer.) (b) The equation of the tangent line to the curve at P(2,-4) is y=