Is #f(x)=1-x-e^(-3x)/x# concave or convex at #x=4#?
1 Answer
Feb 5, 2018
Let's take some derivatives!
Explanation:
For
This simplifies (sort of) to
Therefore
Now let x = 4.
Observe that the exponential is always positive. The numerator of the fraction is negative for all positive values of x. The denominator is positive for positive values of x.
Therefore
Draw your conclusion about concavity.