which of the two functions below has the smallest minimum y-value f(x)=4(x-6)^4+1 g(x)2x^3+28
Accepted Solution
A:
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.