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Finding Inflection Points (Applied Calc Question)

  • Thread starter Sam
  • Start date

Sam

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The problem: Find the inflection points, if any, for the following: f(x) = e^x + x^-1

I know to find inflection points I have to:

1. Compute f''(x)
2. Determine the points in the domain of f for which f''(x) = 0 or f''(x)
does not exist
3. Determine the sign of f''(x) to the left and right of each point x = c
found in step 2. If there is a change in the sign of f''(x) as we move
across the point x = c, then (c, f(c)) is an inflection point of f.

Well, this is what I came up with:

f'(x) = e^x -x^-2
f''(x)= e^x + 2x^-3

Then, I don't know what to do from there because e^x can never be zero, right? but I don't know. My teacher is saying there are inflection points...

Your help is much appreciated!

Sam
 

HallsofIvy

Science Advisor
Homework Helper
41,713
876
Yes, ex is never 0, but an inflection point is NOT where "ex= 0". It is where f"= ex+ 2/x3= 0.

There is no "algebraic" way to solve that equation but it certainly has solutions: using Newton's method or a hand-dandy graphing calculator, we have a zero of f", and an inflection point, for x approximately 0.926.
 

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