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Mean Value Theorem
If a function f is:
continuous on the closed interval
differentiable on the open interval
there is at least one point where the instantaneous rate of change is equal to the average rate of change
Extreme Value Theorem
If a function f is
continuous on the closed interval
it has an absolute maximum and an absolute minimum on the interval
These happen at critical points or endpoints
Critical Point
When the derivative is 0 or doesn’t exist
if the sign changes from positive to negative it’s a local maximum
if the sign changes from negative to positive it’s a local minimum
First Derivative Test
When you plug in intermediate values between the critical points into the derivate to test for a sign change
Concave Up
When the rate of change over an interval is increasing (getting more steep)
Concave Down
When the rate of change over an interval is decreasing (getting less steep)
Second Derivative Test
Test for extrema
If it is positive, the point is concave up and is a minimum
If it is negative, the point is concave down and is a maximum
Inflection Point
Location where the function switches concavity
Second derivative of this point will be 0
Note 
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