Question

Given (x)=-x²+2x,determine F'(x) using first principle

Answer 1

Hello,
which principle?

f(x)=-x²+2x
==>f'(x)= -2x+2

You mean maybe this

$\lim_{h \to 0} \frac{f(x+h)-f(x) } {h}$


f(x+h)=-(x+h)²+2(x+h)= -(x²+2hx+h²)+2x+2h
f(x)=-x²+2x

$\lim_{h \to 0} \frac{f(x+h)-f(x) } {h}=\lim_{h \to 0}\frac{-2hx-h^2+2h}{h}=\lim_{h \to 0}\frac{-2x-h+2}{1}=-2x+2$