posted by lana .
find the max point on the graph f(x) = -1/3x^3 + 3x^2 - 5x
The maximum is where the first derivative is zero, provided the second derivative is negative there.
Solve the equation
f'(x) = -x^2 +6x -5 = 0
-(x-5)(x-1) = 0
x = 5 and x = 1 are either maxima or minima. Use the second derivative test to see which is which.