SOLUTION: f(x)=8x-3x^2 i must indicate if it has a maximum or minimum. how do i go about this

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Question 280076: f(x)=8x-3x^2 i must indicate if it has a maximum or minimum. how do i go about this
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=8x-3x^2 i must indicate if it has a maximum or minimum. how do i go about this
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We need to find the "critical points" by taking the first derivative of f and setting that equal to zero:
f'(x) = 8 - 6x
8 - 6x = 0
x = 4/3
So a max or min occurs at x = 4/3.
The second derivative test tells us if we have a max or min:
f''(x) = -6
Since f''(x) < 0 for all x including x = 4/3 we know x = 4/3 is where a maxiumm occurs. The actual value of the maximum is:
f(4/3) = 8*(4/3) - 3*(4/3)^2