Find b such that f(x)=-4x^2+bx+3 has a maximum value of 50.

Answer 1

The derivative f'(x) of -4x²+bx+3 is the gradient of f(x), which is -8x+b.

At x=50 the function takes a maximum value, so the gradient must be zero, so -8x+b=0 at x=50, which means that b=400.

Check the above: f(x) = -4x² + 400x + 3, so f'(x) = -8x + 400 = 0, so x = 50.