Posted by shannon on Thursday, September 25, 2008 at 6:48pm.
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.
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