Question

Find the turning points of y = 3x power 3 - 9x power 2
and determine their nature.

Answer 1

dy/dx = 9 x^2 + 12 x + 3

so

9 x^2 + 12 x + 3 = 0 for turning point

(9x+3)(x+1) = 0

x = -1/3 and x = -1

I will start the x = -1 point. You do the x = -1/3

the slope is 0 at these points so just find y

if x = -1, y = 3(-1)+6(1)+3(-1)-1

= -1

so tangent is y = -1