Consider the function below.

Question

f(x) = 4x2 - 5x
(a) Find f '(2).


(b) Use the answer in part (a) to find an equation of the tangent line to the parabola y = 4x2 - 5x at the point (2, 6).
y =

Answer 1

y = 4 x^2 - 5 x

y' = 8 x - 5

at x = 2
y'(2) = 16-5 = 11

m = 2
y = m x + b
6 = 2 (2) + b
b = 2
so
y = 2 x + 2