Find Critical Numbers: Easier Way to Solve

[afcwestwarrior]

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

 

[afcwestwarrior]

i know the theorem already

 

[hage567]

What theorem are you referring to?

You take the derivative of the function, set it equal to zero, and solve.

 

[reza]

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.

 

[cDimino]

Aren't points of inflection also critical points?

 

[HallsofIvy]

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.