Hi. I think someone already asked this question, but I am really having a hard time with it.

Functions f(x) and g(x) are shown below:
f(x)=3x^2+12x+16 g(x)=2sin(2x-pi)+4
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.

Question

Hi. I think someone already asked this question, but I am really having a hard time with it. 

Functions f(x) and g(x) are shown below: 
f(x)=3x^2+12x+16      g(x)=2sin(2x-pi)+4
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.

anonymous · Answer

*Find critical poi.nts and use second derivative test
F(x)=6x+12=0 -> x=-2
Since F(x)=6>0, minimum is at -2

g(x)=4cos(4x-pi)=0, -pi/4 -> x= pi/2, 3pi/2 etc...
g(x)=16sin(4x-pi) >0, x= 5pi/8 etc...
g(5pi/8)=2sin(pi/4)+4=4+ sqrt2 > F(-2)=4