Question

The energy expended by a bird per day, E, depends on the time spent foraging for food per day, F hours. Foraging for a shorter time requires better territory, which then requires more energy for its defense.1 Find the foraging time that minimizes energy expenditure if E=0.25F+1.7/f^2

Answer 1

Answer:

Therefore F=2.387 hours gives a minimum value of energy expenditure E.

Step-by-step explanation:

Given that,

The energy expended by a bird per day

$E=0.25 F+\frac{1.7}{F^2}$

Differentiating with respect to F

$E'=0.25 -\frac{3.4}{F^3}$

Again differentiating with respect to F

$E''=\frac{10.2}{F^4}$

Now set E'=0

$0.25 -\frac{3.4}{F^3}=0$

$\Rightarrow \frac{3.4}{F^3}=0.25$

$\Rightarrow F^3=\frac{3.4}{0.25}$

$\Rightarrow F=2.387$

Now $E''|_{F=2.387}=\frac{10.2}{2.387^4}>0$

Since, E''>0 at F=2.387, So at F=2.387 , E has minimum value.

Therefore F=2.387 hours that minimizes energy expenditure.