Question

Find the values of b such that the function has the given maximum value. f(x) = −x2 + bx − 16;
Maximum value: 65

Answer 1

That is a function of a downward parabola, so, the maximum of the function is its vertex. You have a formula to find it out, it says vertex has x = -b/2a = b/2
and replace that x into the function to have y = \(-\dfrac{b^2}{4} +b\dfrac{b}{2}-16 \)
That is maximum value, so that y =65
So you have \(-\dfrac{b^2}{4} +b\dfrac{b}{2}-16=65 \)
solve for b to get the answer