What are the inflections points of y = e 2 x - e x ?
What are the inflections points of ?
Answer & Explanation
Beginner2023-02-22Added 5 answers
By the Chain Rule, the first derivative is and the second derivative is . Inflection points occur at x values where the sign of the second derivative changes (from positive to negative or negative to positive).
Setting leads to . The left-hand side of this equation can be factored as . Since is never zero, it follows that we just need to solve to get .
You can check that changes sign at this point by graphing it. Therefore, there is an inflection point at . The second coordinate of this point can be found by plugging it into the original function to get . The inflection point is therefore .
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