Question

1. Use the first principles formula lim
h -0
f(x + h) f(x)
h
to find the derivative function for the following function: f(x) = -x^2 + 2x^3

Answer 1

\[f'(x)=\lim_{h\to0}\frac{\left(2(x+h)^3-(x+h)^2\right)-\left(2x^3-x^2\right)}{h}\]
Expand those binomials. Most terms will disappear, leaving you with a factor of \(h\) in both numerator and denominator.

Answer 2

check the attachment and tell me if this is correct

Answer 3

Yes, that's all correct.

Answer 4

thank you @SithsAndGiggles

Answer 5

You're welcome