calculate the min or max?

Question

f(x)= -3x^2+2x-2

Answer 1

find relative points

y = -3x2 + 2x -2

dy/dx = -6x + 2

solve for zero

-6x + 2 = 0
-6x = -2
x = 1/3

second derivative test
dy2/dx2 = -6. since it is negative, 1/3 is a max point

y = 3(1/3)^2 + 2(1/3) -2
= 3/9 + 2/3 - 2
= 1 - 2
= -1
(1/3, -1) is your max point

Answer 2

f´(x)= -6x+2= 0 so x=1/3 sign is ++++++ 1/3--------
and f(1/3) =-1/3+2/3-2 =-5/3 is a maximum