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Problem

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Textbook Expert
Textbook ExpertVerified Tutor
3 Dec 2021

Given information

Given the graph of the derivative  of a function :

The given condition is that .

Step-by-step explanation

Step 1.
  • The function  is said to be increasing function in an interval if  or that interval and the function is said to be decreasing function in an interval if   for that interval.
  • Determine the intervals where and from the graph of  .
  • The function has inflection point where that is the function has inflection point where the slope of the tangent to the curve  is 0.
  • Determine the point where the slope of the tangent to the curve is 0.
  • Determine the point of inflection.

From the graph of the function , it can be noticed that for  and  for .

The slope of the tangent to the curve  is 0 is .

Therefore, the point of inflection is  .

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