Given f(x)=3x^2 +1 find: f(x+h)-f(x)/h

Answer 1

I assume that you are being asked to calculate (f(x+h)-f(x))/h,

because it looks like your teacher is preparing you for the definition of derivative.

If your teacher does actually mean f(x+h)-f(x)/h then you can do that using the

same method.

Substitute the definition of f into the expression

(3(x+h)²+1 - (3x²+1))/h =

(3x² + 6xh + 3h² + 1 - 3x² - 1)/h =

(6xh + 3h²)/h =

6x + 3h