# Is #f(x)=x^3-x+e^(x-x^2) # concave or convex at #x=1 #?

##### 1 Answer

Apr 26, 2018

It is convex.

#### Explanation:

The function will be convex if the second derivative is positive, and concave if it is negative.

Weisstein, Eric W. "Second Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SecondDerivativeTest.html

The first derivative is:

The second derivative is:

Calculation detail steps here:

http://calculus-calculator.com/derivative/

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