Question

find and simplify the difference quotient f(x+h)-f(x) divided by h. f(x)=x^2+2x-3

Answer 1

\[\frac{f(x+h) - f(x)}{h} = \frac{(\text{ }(x+h)^2 + 2(x+h) - 3 )- (x^2 + 2x -3)}{h}\]

Answer 2

so expanding the top line:

\[= \frac{(\text{ }x^2 + 2xh +h^2 + 2x +2h - 3 )- (x^2 + 2x -3)}{h}\]

Answer 3

gather together the terms and then divide through by h