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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

Respuesta :

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

[tex]E=0.25 F+\frac{1.7}{F^2}[/tex]

Differentiating with respect to F

[tex]E'=0.25 -\frac{3.4}{F^3}[/tex]

Again differentiating with respect to F

[tex]E''=\frac{10.2}{F^4}[/tex]

Now set E'=0

[tex]0.25 -\frac{3.4}{F^3}=0[/tex]

[tex]\Rightarrow \frac{3.4}{F^3}=0.25[/tex]

[tex]\Rightarrow F^3=\frac{3.4}{0.25}[/tex]

[tex]\Rightarrow F=2.387[/tex]

Now [tex]E''|_{F=2.387}=\frac{10.2}{2.387^4}>0[/tex]

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.

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