Consider the function f(x)=x²-3x-4 Evaluate f ′(-2) using the definition of the derivative?
1 Answer
Mar 8, 2018
We have
#f'(x) = lim_(h->0) (f(x + h) - f(x))/h#
#f'(x) = lim_(h->0) ((x+ h)^2 - 3(x+ h) - 4 - (x^2 - 3x -4))/h#
#f'(x) = lim_(h->0) (x^2 +2xh + h^2 - 3x - 3h - 4 - x^2 + 3x + 4)/h#
#f'(x) = lim_(h->0) (h^2 + 2xh - 3h)/h#
#f'(x) = lim_(h->0) (h(h + 2x - 3))/h#
#f'(x) = lim_(h->0) h + 2x- 3#
#f'(x) = 2x -3#
We would get the same result had we just used the power rule. Now just evaluate.
#f'(-2) = 2(-2) - 3 = -7#
Hopefully this helps!
