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May 24, 2013

# Homework Help: math

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

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

• math - David Q, Monday, September 29, 2008 at 2:44pm

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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