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# A graph of a population of yeast cells in a new laboratory culture as a function of time is shown.(a) Describe how the rate of population increase varies.(b) When is this rate highest?(c) On what intervals is the population function concave upward or downward?(d) Estimate the coordinates of the inflection point.

## $f(x)=\frac{x^{4}+x^{3}+1}{\sqrt{x^{2}+x+1}}$, In Maple, we define $f$ and then use the command$\text { plot (diff (diff }(f, x), x), x=-2 \ldots 2) ;$ In Mathematica, we define $f$and then use $\operatorname{Plot}[\mathrm{Dt}[\mathrm{Dt}[\mathrm{f}, \mathrm{x}], \mathrm{x}],\{\mathrm{x},-2,2\}] .$ We see that $f^{\prime \prime}>0$ for$x<-0.6$ and $x>0.0[\approx 0.03]$ and $f^{\prime \prime}<0$ for $-0.6<x<0.0 .$ So $f$ is $\mathrm{CU}$on $(-\infty,-0.6)$ and $(0.0, \infty)$ and $\mathrm{CD}$ on (-0.6,0.0)

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#### Topics

Derivatives

Differentiation

Volume

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp