##### Find the maximum or minimum value of the function. (Round your answer to two dec

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Find the maximum or minimum value of the function. (Round your answer to two decimal places.)
f(t) = 100 − 9t − 3t2

Jul 8th, 2015

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$\\ f(t)=100-9t-3t^2\\ \\ f(t)=-3t^2-9t+100\\$

So, a = -3 , b = -9 and c = 100

Since a = -3 < 0, the parabola opens downwards and hence the vertex will be the highest point.

Vertex occurs where

$\\ t=\frac{-b}{2a}\\ \\ t=\frac{-(-9)}{2\times(-3)}\\ \\ t=\frac{9}{-6}\\ \\ t=-\frac{3}{2}$

For t = -3/2

$\\ f\bigg(\frac{-3}{2}\bigg)=-3\bigg(\frac{-3}{2}\bigg)^2-9\bigg(-\frac{3}{2}\bigg)+100\\ \\ f\bigg(\frac{-3}{2}\bigg)=-3\times\frac{9}{4}+\frac{27}{2}+100\\ \\ f\bigg(\frac{-3}{2}\bigg)=-\frac{27}{4}+\frac{27}{2}+100\\ \\ f\bigg(\frac{-3}{2}\bigg)=\frac{-27+27\times2+100\times4}{4}\\ \\ f\bigg(\frac{-3}{2}\bigg)=\frac{-27+54+400}{4}\\ \\ f\bigg(\frac{-3}{2}\bigg)=\frac{427}{4}\\ \\ f\bigg(\frac{-3}{2}\bigg)=106.75\\$

So, vertex is (-3/2, 106.75).

Hence, the maximum value of the function is 106.75 .

Maximum value = 106.75

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Jul 8th, 2015

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Jul 8th, 2015
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Jul 8th, 2015
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