List the critical numbers of the following function in increasing order. f(x)=3x^3+3x^2−3x

Question

List the critical numbers of the following function in increasing order.  f(x)=3x^3+3x^2−3x

anonymous · Answer

Take the derivative, find where the derivative is equal to 0 or does not exist.

anonymous · Answer

so 9x^2+ 6x-3. how do i find where it  is = 0 or DNE?

accessdenied · Answer

Set your function equal to zero and solve.  Are you familiar with solving quadratic equations?
  $9x^2 + 6x - 3 = 0$     Solve for the x-values.

accessdenied · Answer

There are a few strategies for solving quadratics.  I will describe my method:
  a)  Try to factor the equation.  If it is factorable, then we can use the property that   A*B = 0  means A = 0 or B = 0 and solve two linear equations.
  b)  If it is not factorable or unclear if it even factors, we can use the quadratic formula.  For an equation in the form $ax^2 + bx + c = 0$, we have:  $$ \qquad x = \frac{\neg b \pm \sqrt{b^2 - 4ac}}{2a} $$As the solutions.