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Question

A certain viral infection causes a fever that typically lasts 6 days. A model of the fever (inF)\left( \text{in}^{\circ} \mathrm{F}\right) on day x,1x6x, 1 \leq x \leq 6 is

F(x)=23x2+143x+96F(x)=-\frac{2}{3} x^{2}+\frac{14}{3} x+96

According to the model, on what day should the maximum fever occur? What is the maximum fever?

Solution

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Answered 4 months ago
Answered 4 months ago
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The model of the viral infection fever (F^\circ F) on day xx is given by, F(x)=23x2+143x+96,1x6.F(x)=-\dfrac{2}{3}x^2+\dfrac{14}{3}x+96,\quad 1\le x\le 6.

We see by the negative in the x2x^2-term that this defines a parabola opening downward, so the maximum revenue is at the vertex. The xx-coordinate of the vertex is x=b2a=1432(23)=72.x=-\dfrac{b}{2a}= -\dfrac{\dfrac{14}{3}}{2(-\dfrac{2}{3})}=\dfrac{7}{2}.

Therefore, the maximum fever occur on the third day.

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