f(x) 3x^2+5x-7. simplify the quotient: f(x+h)-f(x)/h

Question

f(x) 3x^2+5x-7. simplify the quotient: f(x+h)-f(x)/h

Answer 1

f(x) = 3x²+5x-7

 

[f(x+h)-f(x)]/h = [3(x+h)²+5(x+h)-7 - (3x²+5x-7)]/h

 

                     = [3(x²+2xh+h²)+5x+5h-7-3x²-5x+7]/h

 

                     = [3x²+6xh+3h²+5x+5h-7-3x²-5x+7]/h

 

                     = [6xh+3h²+5h]/h

 

                     = h(6x+3h+5)/h

 

                     = 6x + 3h + 5