Question

I do not understand this:

Evaluate and simplify f(x+h)-f(x)/h if
f(x)=x^2-2x

Answer 1

f(x+h) = (x+h)^2 - 2(x+h)
= x^2 + 2hx + h^2 - 2x - 2h

so f(x+h)-f(x)/h
= (x^2 + 2hx + h^2 - 2x - 2h - (x^2-2x))/h
= (2hx + h^2 - 2h)/h
= 2x + h - 2

Answer 2

tutorial(dot)math(dot)lamar(dot)edu/Classes/CalcI/DefnOfDerivative.aspx

lim h->0 ([(x+h)^2-2(x+h)]-[x^2-2x])/h

Answer 3

lim h->0 (2x + h - 2)