What is the maximum value of $4(x + 7)(2 - x)$, over all real numbers $x$?
+14913 What is the maximum value of \(4(x + 7)(2 - x)\), over all real numbers x?
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\(f(x)=4(x + 7)(2 - x)\\ f(x)=4(2x-x^2+14-7x)\\ f(x)=-4x^2-20x+56\\ \frac{df(x)}{dx}=-8x-20=0\\ x_{min}=-2.5\\\color{blue} f(x)_{max}=81\),
The maximum value of \(4(x + 7)(2 - x)\) is 81.
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