Calculus 1 : Relative Minimum
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Example Question #1 : How To Find Relative Minimum On The Interval By Graphing Functions
The following is a list of values at certain points for continuous 
At least 1
At least 2
At most 2
Exactly 1
Exactly 2
At least 2
The mean value theorem states that if continuous 
Example Question #2 : How To Find Relative Minimum On The Interval By Graphing Functions
A relative minimum of a function is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood. These are points in which the first derivative is 0 or it does not exist.
Find the relative minimum of the function
using the following graph and the function.
We notice that this function has 2 extrema which are located at x=-1 and x=0. We could have also of found this by looking at the function itself:
We know that extrema exist when the slope of the function is zero, hence we take the derivative, set it equal to zero, and than solve for x.
The derivative is the following:
Therefore setting both pieces equal to zero we see the following:
Finding out if one of these x values produce a local min or max however requires either the first derivative test, the second derivative test, or analyzing the graph. We see that for a small neighborhood around 
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