Verified Answer :

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

Answer:

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

\(y = 3x^2\)

\(y = 2x^6\)

Step-by-step 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