What real value of t produces the smallest value of the quadratic t^2 -9t - 36?
+14903 What real value of t produces the smallest value of the quadratic t^2 -9t - 36?
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\(\color{BrickRed}f(t)=t^2 -9t - 36\\ \frac{f(t)}{dt}=2t-9\\ 2t-9=0\\ 2t=9\)
\(t=4.5\)
\(V_{smallest}\ of\ (t^2 -9t - 36)\\ =4.5^2-9\cdot4.5-36\\ \)
\(V_{smallest}=-56.25\)
The smallest value of the quadratic \(t^2 -9t - 36\) is -56.25.
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