Question

f(x+h)-f(x)/h when f(x) = x^2 +1

Answer 1

((x+h)^2+1 - (x^2+1))/h
= (x^2+2xh+h^2-x^2-1)/h
= (2xh+h^2)/h (other values cancel out)
= (h(2x-h))/h
= 2x- h (h's cancel out)

Answer 2

hope that helps :)

Answer 3

something went wrong with your signs

Answer 4

\[f(x+h)=(x+h)^2+1=x^2+2xh+h^2+1\]
\[-f(x)=-(x^2+1)=-x^2-1\]
----------------------------------add
\[f(x+h)-f(x)=2xh+h^2\]

Answer 5

\[\frac{f(x+h)-f(x)}{h}=\frac{2xh+h^2}{h}\]

Answer 6

\[\frac{h(2x+h)}{h}\]

Answer 7

Does anything cancel?