Determine the differential quctient fx h fxh fx 3x2 5 fx

Determine the differential quctient f(x + h) - f(x)/h f(x) = 3x^2 - 5 f(x + h) - f(x)/h

Solution

f(x)=3x²-5

f(x+h)= 3(x+h)²-5 = 3x²+3h²+6xh -5

Difference quotient= (f(x+h)-f(x))/h = (3x²+3h²+6xh-5 -3x²+5)/h

                                                           = (3h²+6xh)/h = 3h+6x