Roller Coaster -

F(x)= x^6 - 4x^5 + 3x^4 + 6x^3 - 4x^2 - 12x

F'(x)=6x^5 - 20x^4 + 12x^3 + 18x^2 - 8x - 12=0

x= 1.15, -0.88, 1, 0.816, -1.5

f(1.15) = 1.15^6 - 4(1.15)^5 + 3(1.15)^4 + 6(1.148)^3 - 4(1.15)^2 - 12(1.15)

          = -10.43

f(-0.88)= (-0.88)^6 - 4(-0.88)^5 + 3(-0.88)^4 + 6(-0.88)^3 - 4(-0.88)^2 - 12(-0.88)

           =-13.57

f(1) = 1^6 - 4(1)^5 +3(1)^4 + 6(1)^3 - 4(1)^2 -12(1)

      = -10

f(-0.816) = -0.816^6 - 4(-0.816)^5 + 3(-0.816)^4 + 6(-0.816)^3 - 4(-0.816)^2 - 12(-0.816)

           = -3.73

f(-1.5) = (-1.5)^6 - 4(-1.5)^5 + 3(-1.5)^4 + 6(-1.5)^3 - 4(-1.5)^2 -12(-1.5)

          = 46.82

The critical points for this function, which will have 3 local minima and 2 local maxima are: (1.15,-10.43), (-0.88,-13.57), (1,-10), (-0.816,-3.73) & (-1.5, 46.82)