Answer:
3x^2 +3hx +h^2 +3
Step-by-step explanation:
As with any function evaluation, substitute the argument for x and simplify.
Quotient
Using the definition of f(x), and using the given arguments, we have ...
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{((x+h)^3+3(x+h))\ -\ (x^3+3x)}{h}\\\\=\dfrac{((x^3+3hx^2+3h^2x+h^3)+(3x+3h))-x^3-3x}{h}\\\\=\dfrac{(1-1)x^3+3hx^2+(3h^2+3-3)x+(h^3+3h)}{h}=\dfrac{3hx^2+3h^2x+h(h^2+3)}{h}\\\\=\boxed{3x^2+3hx +h^2+3}[/tex]
