What is the maximum value of the function f (X) = - 3X^2+18x-10

The local or global extrema will occur when velocity, dy/dx, is equal to zero.

dy/dx=-6x+18

d2y/dx2=-6

Since acceleration, d2y/dx2, is a constant negative, when dy/dx=0, y is at an absolute maximum value ...

dy/dx=0 only when - 6x+18=0, - 6x=-18, x=3

And the maximum value is:

f (3) = - 3 (3^2) + 18 (3) - 10

f (3) = 17