Answer:
[tex]-\frac{45}{16}[/tex]
Step-by-step explanation:
[tex]g(x)=\frac{x^{2} -7x+1}{4}[/tex]
Take the derivate of g:
[tex]g'(x)=\frac{x-7}{4}[/tex]
Find x that:
g'(x)=0
solving:
[tex]\frac{2x-7}{4}=0\\x=\frac{7}{2}[/tex]
This x give the least possible value that are g(7/2):
[tex]g(\frac{7}{2}) =-\frac{45}{16}[/tex]
