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# help

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What real value of t produces the smallest value of the quadratic t^2 -9t - 36?

Apr 25, 2020

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What real value of t produces the smallest value of the quadratic t^2 -9t - 36?

Hello Guest!

$$\color{BrickRed}f(t)=t^2 -9t - 36\\ \frac{f(t)}{dt}=2t-9\\ 2t-9=0\\ 2t=9$$

$$t=4.5$$

$$V_{smallest}\ of\ (t^2 -9t - 36)\\ =4.5^2-9\cdot4.5-36\\$$

$$V_{smallest}=-56.25$$

The smallest value of the quadratic $$t^2 -9t - 36$$ is -56.25.

!

Apr 25, 2020
edited by asinus  Apr 25, 2020