### Home > CALC > Chapter 8 > Lesson 8.2.2 > Problem8-84

8-84.

Multiple Choice: $f(x) = e^{−x} − x^3 + 3x^2 − 10x$ changes concavity at $x =$ ?

1. $−2.03$

1. $−1.54$

1. $0.32$

1. $1.06$

1. $2.35$

Concavity change might (or might not) happen where $f^{\prime\prime}(x) = 0$. Remember, you must confirm that concavity CHANGES at that candidate by detecting a sign change in the 2nd-derivative before and after the candidate, or by confirming that 3rd-derivative at the candidate is not equal to $0$.