Question

A fish swims at a speed v relative to the water, against a current of 3 mi/h. Using the mathematical model of energy expenditure E(v) = 2.73v^3 - 6v - 3, find the value of v that minimizes the energy required to swim a distance of 6 mi.

Answer 1

To find the value of v that minimizes the energy required to swim a distance of 6 mi, we need to find the value of v that minimizes the energy expenditure function E(v) = 2.73v^3 - 6v - 3.

Step-by-step explanation:

To find the value of v that minimizes the energy required to swim a distance of 6 mi, we need to find the value of v that minimizes the energy expenditure function E(v) = 2.73v^3 - 6v - 3. To do this, we can take the derivative of E(v) with respect to v and set it equal to zero:

dE(v)/dv = 0

Solving this equation will give us the value of v that minimizes the energy required to swim a distance of 6 mi.