Question

F(x + h) – f(x)

For the function f, construct and simplify the difference quotient
h
9) f(x) = 14 - 2x3

Answer 1

9514 1404 393

Answer:

-6x² -6xh -2h²

Explanation:

Apparently, you want ...

(f(x+h) -f(x))/h

for f(x) = 14 -2x³

That difference quotient is ...

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