Pontos Críticos

[latex]\mathrm{S(t)=-0,00003237t^5 + 0,0009037t^4 - 0,008956 t^3+ 0,03629t^2 - 0,04485t + 0,4074 }[/latex]

[latex]\mathrm{\frac{dS(t)}{dt}=-0,00016185t^4+0,0036148t^3-0,026868t^2+0,07258t-0,04485}[/latex]

[latex]\mathrm{Pelo\ M\acute{e}todo\ do\ Intervalo\ Fechado,pois\ \frac{dS(t)}{dt}\ \exists \ \forall\ t\ e\ S(t)\ \acute{e}\ continua\ em\ 0\leq t\leq 10,o\ pt.\ critico\ ocorre\ em:}[/latex]

[latex]\mathrm{\ \frac{dS(t)}{dt}=0\to -0,00016185t^4+0,0036148t^3-0,026868t^2+0,07258t-0,04485=0\to t\approx\left\{\begin{matrix}
\mathrm{0,8627\ anos}\\
\mathrm{4,5846\ anos}\\
\mathrm{7,3343\ anos}\\
\mathrm{9,5527\ anos}
\end{matrix}\right. }[/latex]

[latex]\therefore {\left\{\begin{matrix} \mathrm{S(0,8627)\approx 0,3904}\\ \mathrm{S(4,5846)\approx 0,4352}\\ \mathrm{S(7,3343)\approx 0,4251}\\ \mathrm{S(9,5527)\approx 0,4338} \end{matrix}\right.}[/latex]

[latex]\mathrm{Do\ intervalo:\ S(0)=0,4074\ e\ S(10)\approx 0,4319 }[/latex]

[latex]\mathrm{No\ intervalo\ 0\leq t\leq 10,S(t)=S_{m\acute{a}x}=0,4352,isto\ \acute{e}, ap\acute{o}s\ t\approx4,5846\ anos\ (1993+4,5846\approx1998 ) .}[/latex]

[latex]\mathrm{De\ forma\ an\acute{a}loga,S(t=0,8627)=S_{min}=0,3904.\ Portanto,1993+0,8627\approx 1994.}[/latex]