Answer:
The value of v that minimizes E is v = 3u/2.
Step-by-step explanation:
The given function is;
E(v) = av³L/(v-u)
Applying the quotient rule yields;
dE/dv = [(v-u)•3av²L - av³L(1)]/(v - u)²
By expanding and setting it to zero, we obtain;
[3av³L - 3av²uL - av³L]/(v - u)² = 0
Resulting in;
(2av³L - 3av²uL)/(v-u)² = 0
Multiplying both sides by (v-u)² gives;
(2av³L - 3av²uL) = 0
This means that 2av³L = 3av²uL
Upon simplifying, we have;
2v = 3u.
Thus, v = 3u/2.