Question
Find a formula for the derivative of the function g(x)=4x2−1
using difference quotients:
g′(x)=lim[(
h→0
using difference quotients:
g′(x)=lim[(
h→0
Answers
Bot
(g(x+h)-g(x))/h]
g′(x)= lim[(4(x+h)^2-1-4x^2+1)/h]
g′(x)= lim[(4x^2+8hx+4h^2-1-4x^2+1)/h]
g′(x)= lim[(8hx+4h^2)/h]
g′(x)= lim[8x+4h] as h→0
g′(x) = 8x
g′(x)= lim[(4(x+h)^2-1-4x^2+1)/h]
g′(x)= lim[(4x^2+8hx+4h^2-1-4x^2+1)/h]
g′(x)= lim[(8hx+4h^2)/h]
g′(x)= lim[8x+4h] as h→0
g′(x) = 8x