Mathematics
Differential Calulus Absolute Max and Min

Question Description

I’m working on a Calculus question and need guidance to help me study.

A disease arrives, % of infected is max after 8 days.  Evaluate for p.

p(t)=9te^-t/8

t=8

how do I evaluate for p?

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Final Answer

So you can verify that max is at t=8 by taking the derivative of p(t) and setting it equal to zero (i.e., calculate t-value where p'(t)=0).

p'(t) = 9*e^(-t/8) + (9t)*(-1/8)*(e^(-t/8)) = 9*e^(-t/8)*(1-t/8)

For max, set p'(t) = 0; thus t=8

Now, we just need to plug t=8 into the original equation for p(t);

Thus: p(8) = 9*8*e^(-8/8) = 9*8/e = 72/e (or aprox., 26.4873)

Alex Z (997)
Duke University

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