Question

Identify the monomial function(s) that have a minimum. y = 5x y = x3 y = –2x6 y = 4x4 y = 3x2 y = 2x6

Answer 1

tex]y = 4x^4[/tex]

`y = 3x^2`

`y = 2x^6`

Explanation:

LEts check with each function

`y = 5x` , it is a linear function.

Linear function does not have minimum

`y = x^3`, Cubic parent function does not have minimum

`y = -2x^6`, we have -2 (negative) . Leading coefficient is negative so, there will be a maximum

`y = 4x^4`,leading coefficient is positive so it have a minimum

`y = 3x^2`, leading coefficient is positive so it have a minimum

`y = 2x^6`, leading coefficient is positive so it have a minimum

Answer 2

y = 5x - This does not have a minimum.
y = x3 - This does not have a minimum
y = –2x6 - This does not have a minimum.
y = 4x4 - This has a minimum
y = 3x2 - This has a minimum
y = 2x6 - This has a minimum

Functions with the positive leading coefficient and even exponent will have a minimum