Evaluate The Limit

Question

lim h → 0

((−6 + h)² − 36h)/h

Answer 1

as h approaches zero, the limit = -12

f(x) = x^2

f'(x) = 2x

f'(-6) = 2(-6) = -12

f(x+h)x-f(x) = x^2 +2xh +h^2 -x^2 = 2xh+h^2

(2xh +h^2)/h = 2x + h

limit of 2x+h as h approaches zero = 2x

when x = -6, the limit = 2(-6) = -12