Find Critical Numbers: Easier Way to Solve

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how do you find critical numbers, and do you have to keep on plugging in a number until you find zero or is their an easier way
 
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i know the theorem already
 
What theorem are you referring to?

You take the derivative of the function, set it equal to zero, and solve.
 
usually we take derivative of function and set it equal to 0 like hage567 said
for example you consider this function
y=x.x+x=x(2)+x
y'=dy/dx
y'=2x+1
for finding the critical number we set it to zero
y'=0
=> 2x+1=0
=> 2x=-1
=> x=-1/2
-1/2 is critical number for this function
and one of its usage is for finding the MAX. and MIN. of a function.
 
Aren't points of inflection also critical points?
 
No. Critical points are where either the derivative is 0 or where the derivative does not exist. Points of inflection are where the secondderivative changes sign. That has to be where the second derivative is 0 or does not exist although not all such points are inflection points.

For example, if f(x)= x3- 3x, then df/dx= 3x2- 3 so the critical points are x= 1 while d2f/dx2= 6x. The only inflection point is at x= 0.
 
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