Question

AP Calculus ab question: what is the derivative function, f'(x), using the definition of derivative for : f(x) = 3X^2 + 1. Please show your work with the method shown below:

f'(x)= lim (h->0) [f(x+h) - f(x)] /h

Answer 1

Answer: f'(x)=6x

Explanation:

f'(x)= lim (h->0) [f(x+h) - f(x)] /h

f'(x)= lim (h->0) [3(x+h)^2 + 1 - (3x^2 + 1)] /h

f'(x)= lim (h->0) [3(x^2+2hx+h^2) + 1 - 3x^2 - 1] /h

f'(x)= lim (h->0) [3x^2+6hx+3h^2 - 3x^2] /h

f'(x)= lim (h->0) [6hx+3h^2] /h

f'(x)= lim (h->0) [6x+3h]

f'(x)= [6x+3(0)]

f'(x)=6x