Question

Given the function f(x)=2x^2-3x, calculate f(a+h)-f(a)/h

Answer 1

`f(x)=2x^2-3x`


`( f(a+h)-f(a))/(h)`


`= (2(a + h)^2 - 3(a + h) - (2a^2 - 3a))/(h)`


`= (2(a^2 + 2ah + h^2) - 3a - 3h - 2a^2 + 3a)/(h)}`


`= (2a^2 + 4ah + 2h^2 - 3a - 3h - 2a^2 + 3a)/(h)}`


`= (4ah + 2h^2 - 3h)/(h)}`


`= (h(4a + 2h - 3))/(h)}`


`= 4a + 2h - 3`