Question

The function f(x) = -x^4 + 3 does not have an absolute maximum. TRUE OR FALSE?

Answer 1

We have to determine if the function has the absolute value maximum:

F(x)=-x^4+3 ⮕ (1)

The plot of the function is (1)


The f(x) has the absolute mad, and it is at x=0


Solution


False

Answer 2

False.

Explanation:

The equation f(x) =
`-x^4` + 3 has a maximum interval of (0, 3).

First simplify the equation:

f(x) =
`-4x^3`

Then find the intervals:

Increasing -∞<x<0, Decreasing 0>x>∞

Plug x = 0 into
`-x^4`+3: 3

Therefore the maximum interval of
`f(x) = -x^4 + 3` is (0, 3)