Question

F(x + h) – f(x)

Answer 1

9514 1404 393

Answer:

  -6x² -6xh -2h²

Step-by-step explanation:

Apparently, you want ...

  (f(x+h) -f(x))/h

for f(x) = 14 -2x³

That difference quotient is ...

  $\dfrac{f(x+h)-f(x)}{h}=\dfrac{(14 -2(x+h)^3)-(14-2x^3)}{h}\\\\ =\dfrac{14-2(x^2 +3x^2h+3xh^2+h^3)-14+2x^3}{h}=\dfrac{-6x^2h-6xh^2-2h^3}{h}\\\\ =\boxed{-6x^2 -6xh-2h^2}$