Question

Which of the two functions below has the smallest minimum y-value f(x)=4(x-6)^4+1 g(x)2x^3+28

Answer 1

Answer:

The function g(x) has smallest minimum y-value.

Step-by-step explanation:

The given functions are

$f(x)=4(x-6)^4+1$

$g(x)=2x^3+28$

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.

$(x-6)^4\geq 0$

Multiply both sides by 4.

$4(x-6)^4\geq 0$

Add 1 on both the sides.

$4(x-6)^4+1\geq 0+1$

$f(x)\geq 1$

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.