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Calculus

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Could someone explain this question please.

Suppose the population (in thousands of a certain species of insect after t months is described by the function p(t)=4t+ (100t)/(t^2+400) + 500. Determine the maximum population in the first three months.

  • Calculus - ,

    when x is small (as in the interval [0,3]

    100t/(t^2+400) is just basically t/4
    so, p(t) looks a lot like 4t + t/4 + 500
    that's just a line, so the max and min are at the ends of the interval.

  • Calculus - ,

    If I factor it out, it'll be 17t/4 + 500.

    then plug in 3

    17(3)/4+500=512 x 1000

    =512,750.

    therefore the population would be 512,750?

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