Identifying Turning Points (Local Extrema) for a Function
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Key Questions

For a differentiable function
#f(x)# , at its turning points,#f'# becomes zero, and#f'# changes its sign before and after the turning points.
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Answer:
See below.
Explanation:
To find extreme values of a function
#f# , set#f'(x)=0# and solve. This gives you the xcoordinates of the extreme values/ local maxs and mins.For example. consider
#f(x)=x^26x+5# . To find the minimum value of#f# (we know it's minimum because the parabola opens upward), we set#f'(x)=2x6=0# Solving, we get#x=3# is the location of the minimum. To find the ycoordinate, we find#f(3)=4# . Therefore, the extreme minimum of#f# occurs at the point#(3,4)# . 
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Questions
Videos on topic View all (4)
Graphing with the First Derivative

1Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

2Identifying Stationary Points (Critical Points) for a Function

3Identifying Turning Points (Local Extrema) for a Function

4Classifying Critical Points and Extreme Values for a Function

5Mean Value Theorem for Continuous Functions