For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current u (u < v), then the time required to swim a distance L is L/(v - u) and the total energy E required to swim the distance is given by the formula below, where a is the proportionality constant.
E(v) = av^3 L/(v - u)
Determine the value of v that minimizes E. (Note: This result has been verified experimentally.)

The value of v = that minimize E.

Step-by-step explanation:

The function that gives the energy lost by a fish E(v) moving with a velocity v against the water velocity u up to a distance L is given by

, where a is a proportionality constant.

Now, for E(v) to be minimum the condition is

⇒

⇒

⇒ 3v³ - 3v²u - v³ = 0

⇒ 2v³ = 3v²u

⇒ v =

Therefore, the value of v = that minimizes E. (Answer)

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

hello,

as we don't know if g(x) is continue,

answer b

f(x)=2x²-8x+1=2(x²-4x+4)+1-8=2(x-2)²-7

vertex is (2,-7) ( a minimum since coefficient of x² is > 0)