Which of the two functions below has the smallest minimum y-value?

f (x) = x4 - 2

g (x) = 3x3 + 2

To get the minimum y-value, the functions must be differentiated and equated to zero. The resulting value of x is then substituted to the original functions to get the minimum/maximum value of x.

For f (x) = x4 - 2

df (x) / dx = 4x3 = 0

So, x = 0

f (0) = - 2

For g (x) = 3x3 + 2

dg (x) / dx = 9x2 = 0

x = 0

g (0) = 2

Therefore, f (x) the smallest minimum y-value.