+36916 This is a dome shaped parabola due to the negative leading coefficient
the 'x' value of the vertex will be found by - b/2a where b = 9 and a =-3
use this value of 'x' in the equation to find the 'y' value of the vertex which will be the function's maximum value.....
+14905 Find the maximum value of the function f(x) = -3x^2 + 9x + 7.
Hello Guest!
The extremes of a function are at the zeros of the 1st derivative of the function.
\(f(x) = -3x^2 + 9x + 7\\ \frac{df(x)}{dx}=-6x+9=0\\ x_{max}=1,5\)
\(y = -3x^2 + 9x + 7\\ y=-3\cdot 1.5^2+9\cdot 1.5+7\)
\(y_{max}=13.75\)
\(P_{max}(1.5,\ 13.75)\)
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