Answer:
The difference between the maximum and minimum is
Step-by-step explanation:
Since p = 10-q, we can replace p in the expression and we get a single-variable function
Taking the derivative with respect to q and using the rule for the derivative of a product
Critical point (where f'(q)=0)
Assuming q≠ 0 and q≠ 10
To check this is maximum, we take the second derivative
and
f''(625/63) < 0
so q=625/63 is a maximum. For this value of q we get p=5/63
The maximum value of
is
The minimum is 0, which is obtained when q=0 and p=10 or q=10 and p=0
The difference between the maximum and minimum is then