Question

How do I show that, for x > 0, f(x) = 1/x^3 - x^3 is a decreasing function?

Answer 1

@Luigi0210

Answer 2

Hmm, would you use inflection points?

Answer 3

Find the derivative

Answer 4

Ok, so I show that the derivative of the function will always be negative for x > 0, and this will prove that the function is decreasing.

Answer 5

Yes

Answer 6

So dy/dx = -3/x^4 - 3x^2. Therefore, as this will always be negative, the function is decreasing for x > 0.

Answer 7

Thanks guys!