Question

Which monomial function has a maximum value?
(Can anyone explain how you can tell?)

y=-6x^3
y=-5x^4
y=5x^6
y=6x^5

Answer 1

The most straightforward method would be graphing each one, either by hand or by a graphing calculator.
Of course, that is evading the intuition gained from understanding it.

A maximum value is a point where all points nearby have a lower y-value. f(c) > f(x) for all x in an interval.
A polynomial y = ax^n with odd degree n has no maximum or minimum; it slopes upwards on one side of the graph and downwards going the other way.

The only case where there is an extreme point is when n is even. That graph creates a bowl-shape, like a parabola.