SOLUTION: good day sorry could not find Calculus in the list. It's differentiation. Calculate the turning points 3x� - 6x� -9 = 0 The answers are (0:9) and (4/3:-12.55)

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Question 980208: good day
sorry could not find Calculus in the list. It's differentiation.
Calculate the turning points
3x� - 6x� -9 = 0
The answers are (0:9) and (4/3:-12.55)

Found 3 solutions by Cromlix, ikleyn, rothauserc:
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website!
Hi there,
y = 3x^3 - 6x^2 - 9
dy/dx = 9x^2 - 12x
dy/dx = 0
9x^2 - 12x = 0
3x(3x - 4) = 0
3x = 0
x = 0
Substituting x = 0
into f(x)
3x^3 - 6x^2 - 9
3(0)^3 - 6(0)^2 - 9
= -9
Turning point (0, -9)
.......
(3x - 4) = 0
x = 4/3
Substituting x = 4/3
into f(x)
3x^3 - 6x^2 - 9
3(4/3)^3 - 6(4/3)^2 - 9
- 12.55
Turning point (4/3, -12.55)
Hope this helps:-)

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!

The turning point of a function is the point where the derivative of the function is equal to zero.

The derivative of the function = is = .
So, its turning points are those where the coordinate (variable) x satisfies the equation

= .

They are = and = = .

The points (,) and (,) are yours turning points.

Calculate yourself the values of    and .

Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
derivative of 3x� - 6x� -9 is
9x^2 - 12x =
3x*(3x - 4)
now set it = to 0 and solve
3x * (3x - 4) = 0 and
we have x = 0 or x = 4/3
*****************************************************************************
turning points are determined by substituting for x in original equation
turning points are (0, -9) which is local max and (-4/3, -113/9) which is local min