Find and simply

Question

If f(x)=x^2-3x-5 find and simply f(x+h)-f(x)/h

Answer 1

This is a difference quotient problem.

You must first find each of the terms:

f(x+h) = (x+h)^2 - 3(x+h) -5 = x^2 +2xh +h^2 -3x -3h -5

f(x) = x^2 - 3x -5

f(x+h) - f(x) = (x^2 +2xh +h^2 -3x -3h -5) - (x^2 - 3x -5) = 2xh + h^2 -3h

[f(x+h) - f(x)] / h = (2xh + h^2 - 3h )/ h = 2x +h -3