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)(-2hx-h^2+2h)/(h)=\lim_(h \to 0)(-2x-h+2)/(1)=-2x+2`