- #1

BrownianMan

- 134

- 0

*Show that the function f(x) = x^21 + x^11 + 13x does not have a local maximum or minimum.*

So f '(x) = 21x^20 + 11x^10 + 13.

My reasoning is as follows:

Since the exponents (10 and 20) are even, 21x^20 and 11x^10 can never be negative, and thus, summing them can never produce a negative number to make the expression 0 = 21x^20 + 11x^10 + 13 true. So there are no critical numbers, and therefore no local max or min.

Would this be correct?