Answer:
Value of v that minimizes E is v = 3u/2
Step-by-step explanation:
We are given that;
E(v) = av³L/(v-u)
Now, using the quotient rule, we have;
dE/dv = [(v-u)•3av²L - av³L(1)]/(v - u)²
Expanding and equating to zero, we have;
[3av³L - 3av²uL - av³L]/(v - u)² = 0
This gives;
(2av³L - 3av²uL)/(v-u)² = 0
Multiply both sides by (v-u)² to give;
(2av³L - 3av²uL) = 0
Thus, 2av³L = 3av²uL
Like terms cancel to give;
2v = 3u
Thus, v = 3u/2