Question

1. Let f(x)=x^3-2x. Simplify the expression f(x+h)-f(x)/h
2. Let f(x)=3x+2 and g(x)=x/x+1
3. Let f(x)=2x^2. Simplify the expression f(x+h)-f(x)/h

Answer 1

what you need is replace x by (x+h)
x^3-2x
=[((x+h)^3-2(x+h))-(x^3-2x)]/h
=[(x^3+3x^2h+3xh^2+h^3)-(2x+2h)-(x^3-2x)]/h
=[(x^3+3x^2h+3xh^2+h^3-2x-2h-x^3+2x)]/h
=[3x^2h+3xh^2+h^3-2h)]/h
=h[3x^2+3xh+h^2-2)]/h
=3x^2+3xh+h^2-2)
if you used the limit when h->0 the answer should be 3x^2-2 which is the derivative

Answer 2

# 2 is not clear
#3 as # 1