Functions f(x) and g(x) are shown below: .

f(x) f(x) = 3x2 + 12x + 16
g(x) 16g(x) = 2 sin(2x - π) + 4.
using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.

       First we will find the derivative of each function and equate it to zero.
       f` ( x ) = 6 x + 12
       6 x + 12 = 0
       6 x = - 12
       x = - 2
       f ( - 2 ) 0 12 - 24 + 16 = 4
       f ( x ) min = 4
       g` ( x ) = 4 cos (  2 x - π )
       4 cos ( 2 x - π ) = 0
       cos ( 2 x - π ) = 0
       2 x - π = 3π / 2
       2 x = 5π /2
       x = 5π/4
       g ( 5π/4 ) = 2 sin ( 5π/2 - π ) + 4 = 2 ( sin 3π/2 ) + 4 = -2 + 4 = 2
       g ( x ) min = 2 ( this is the smallest minimum value )

What’s the improper fraction?