Question

How do you find the exact relative maximum and minimum of the polynomial function of `y=x^3`?

Answer 1

`x in (-oo, oo)`. There are no extrema at all..

Explanation:

`y'=3x^2 and y'' ==x` are 0 at `x = 0. y'''= 6 > 0.`

So. y is neither a maximum nor a minimum at x = 0.

Note that y'' = 6x > 0 for x > 0 and < 0 for x < 0.

Origin is a point of inflexion wherein y'changes sign and the tangent

y = 0 crosses the curve..

Also, `x in (-oo, oo`) .