we are given
[tex]F(d)=0.77d^2-1.32d-9.31[/tex]
where
F is the number of board feet
d is the diameter (in inches) of the log
Since, we have to minimize F
so, firstly we will find it's derivative
[tex]F'(d)=0.77\times 2d-1.32\times 1-0[/tex]
[tex]F'(d)=1.54d-1.32[/tex]
now, we can set it to 0
and then we can solve for d
[tex]F'(d)=1.54d-1.32=0[/tex]
[tex]1.54d-1.32=0[/tex]
so, we get diameter as
[tex]d=\frac{6}{7}inch[/tex]..............Answer
