Using the formula lim h approaches 0 f(x+h)-f(x)/h, find the derivative of f(x)=2x^2+4x
2 answers
It's 4x+4
f(x+h) = 2(x+h)^2 + 4(x+h)
= 2x^2 + 4xh + 2h^2 + 4x + 4h
f ' (x) = lim (2x^2 + 4xh + 2h^2 + 4x + 4h - 2x^2 - 4x)/h , as h ---> 0
= lim (4xh + 2h^2 + 4h)/h
= lim h(4x + 2h + 4)/h
= lim 4x + 2h + 4 , as h --> 0
= 4x + 4
= 2x^2 + 4xh + 2h^2 + 4x + 4h
f ' (x) = lim (2x^2 + 4xh + 2h^2 + 4x + 4h - 2x^2 - 4x)/h , as h ---> 0
= lim (4xh + 2h^2 + 4h)/h
= lim h(4x + 2h + 4)/h
= lim 4x + 2h + 4 , as h --> 0
= 4x + 4
1 answer