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Solve the given problems by finding the appropriate derivative.A computer analysis showed that the population density $D$ (in persons/km $^{2}$ ) at a distance $r$ (in $\mathrm{km}$ ) from the center of a city is approximately $D=200\left(1+5 e^{-0.01 r^{2}}\right)$ if $r<20 \mathrm{km} .$ At what distance from the city center does the decrease in population density $(d D / d r)$ itself start to decrease?

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 8

Applications

Derivatives

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Okay, so we want to find our rate of change of the population infected at time. Cheese equal to 32 Here. We're gonna take the derivative at time. Three. So this is deep within our limits as t approaches three t squared plus two t. I know we need p of three that you go through three squared, plus two times three, which is six. So that's equal to 15. So that's minus 15 over T minus three. So in our noon Rita, we contracted us into a T plus five times T minus three. Looking counsel outs are like terms and how Using jacks up, we get three plus five, which is equal to eight.

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