given fxx22x4 find the difference quotient fxhfxh h can not

given f(x)=x²+2x-4

find the difference quotient f(x+h)-f(x)/h , h can not equal 0

Solution

f(x) = x²+2x-4

==> f(x+h) = (x+h)²+2(x+h)-4

==> f(x +h) = x² + 2xh + h² +2x + 2h -4

f(x +h) - f(x) = (x² + 2xh + h² +2x + 2h -4) - ( x²+2x-4)

==> f(x +h) - f(x) = x² + 2xh + h² +2x + 2h -4 - x² -2x +4

==> f(x +h) - f(x) = 2xh + h² + 2h = h(2x + h + 2)

==> [ f(x +h) - f(x)]/h = h(2x + h + 2)/h

==> [ f(x +h) - f(x)]/h = 2x + h + 2