SOLUTION: find the equation of the tangent line to the graph of a. f(x) = -2x^2+3x-2, at x=-2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: find the equation of the tangent line to the graph of a. f(x) = -2x^2+3x-2, at x=-2      Log On


   

Question 746904: find the equation of the tangent line to the graph of
a. f(x) = -2x^2+3x-2, at x=-2
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
First obtain your y coordinate by
substituting x = -2 into f(x)
f(x) = -2(-2)^2 + 3(-2) - 2
= -8 -6 -2
= -16 Coords are: {-2, -16}
Differentiate f(x)
f'(x) = - 4x + 3
Substitute x = -2 into f'(x)
-4(-2) + 3 = 11 (gradient)
Using y - b = m(x - a)
y + 16 = 11(x + 2)
y = 11x + 22 - 16
y = 11x + 6