Answer:
The function g(x) has smallest minimum y-value.
Step-by-step explanation:
The given functions are
[tex]f(x)=4(x-6)^4+1[/tex]
[tex]g(x)=2x^3+28[/tex]
The degree of f(x) is 4 and degree of g(x) is 3.
The value of any number with even power is always greater than 0.
[tex](x-6)^4\geq 0[/tex]
Multiply both sides by 4.
[tex]4(x-6)^4\geq 0[/tex]
Add 1 on both the sides.
[tex]4(x-6)^4+1\geq 0+1[/tex]
[tex]f(x)\geq 1[/tex]
The value of f(x) is always greater than 1, therefore the minimum value of f(x) is 1.
The minimum value of a 3 degree polynomial is -∞. So, the minimum value of g(x) is -∞.
Since -∞ < 1, therefore the function g(x) has smallest minimum y-value.
