Question

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

can someone help me ?

Answer 1

If \(f(x)=x^2+1\), then \(f(x+h)=(x+h)^2+1=x^2+2xh+h^2+1\).

So you have
\[\frac{f(x+h)-f(x)}{h}=\frac{(x^2+2xh+h^2+1)-(x^2+1)}{h}\]
Simplify from here.

Answer 2

ohhhh, okay I was confused as to whether i was plugging the x^2+1 in or the (x+h)... thank you for clearing that up! after i simplified I got 2xh+h^2/h?

Answer 3

Keep simplifying.... you have a common factor there that you can reduce. :)