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

`y=-5x^4`

Explanation:

Remember that a maximum value (global) of a function is the bigest value that the function takes.

For see the values of the functions you can see its graphs.

I have uploaded the graphs of the functions in the question and you can see it, and then convince yourself why the answer is y=-5x^4.

Also you have the fact that the functions of the form
`y=kx^n` have a maximum value only if
`n` is an even natural number and k is a negative real number.

Answer 2

To determine which of the following monomial function has a maximum value, you have to assume the value of x. Let us say the value of x is 2. Substitute 2 for all x’s in the monomial function.

y=-6x^3 = -6(2)^3 = -48
y=-5x^4 = -5(2)^4 = -80
y=5x^6 = 5(2)^6 = 320
y=6x^5 = 6(2)^5 = 192 Therefore, the monomial function with the maximum value is y = 5x^6