 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? Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service. 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)
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