Question 1155423: Find the critical points of the following function.
f(x)=x^2sqrt(x+14)
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! Suppose that x=c is a critical point of  .
If  ' to the left of  and ' to the right of , then is a local maximum.
If ' to the left of and ' to the right of  , then is a local minimum.
If ' is the same sign on both sides of then is neither a local maximum nor a local minimum.
 .....derivate
apply the Product Rule:  '= '*  +* '
equate to zero and solve for 
 -> will be zero if
 -> complex solution, derivative is undefined
if  derivative is undefined
Critical points are points where the function is defined and its derivative is zero or undefined
 ,  ,  -> a critical points
Identify critical points not in f (x ) domain :  is [ )
maximum is at: ( , )
minimum is at: (,)
minimum is at: (,) and (,)
maximum is at ( , )
 is monotone in intervals:
(,) -> is increasing
(,)-> is decreasing
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