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I'm going to assume you mean F(x) = -2x2 + 10x + 6 as -2x plus 10x = 8x...
First differentiate -2x2 + 10x + 6:
dy/dx = -4x + 10
Set dy/dx = 0:
-4x + 10 = 0
Find x:
10 = 4x
2.5 = x
Find y at x =2.5:
y = -2(2.5)2 + 10(2.5) + 6 = -12.5 + 25 +6 = 18.5
So max or min is at (2.5, 18.5)
To find out whether it is max or min differentiate twice:
d2y/dx2 = -4
If its negative, point will be a maximum
If its positive, point will be a minimum.
In this case, a maximum occurs at (2.5, 18.5).
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