Question

For the function f ( x ) = 3x² + 3x , evaluate and simplify. f ( x + h ) − f ( x )/ h

Answer 1

The function f is given by:

`\begin{gathered} f(x)=3x^2+3x \\ f(x+h)=3(x+h)^2-3(x+h) \\ f(x+h)=3(x^2+2xh+h^2)-3(x+h) \\ f(x+h)=3x^2+6xh+3h^2-3x-3h \end{gathered}`

Therefore,

`\begin{gathered} (f(x+h)-f(x))/(h)=(3x^2+6xh+3h^2+3x-3h-(3x^2+3x))/(h) \\ (f(x+h)-f(x))/(h)=(6xh+3h^2+3h)/(h)=6x+3+3h \end{gathered}`

Therefore, the correct answer is 6x + 3 + 3h