For what values of x is the graph of y=xe^−4x concave down?
We have a product of functions, so we use the product rule.
.
.
We require that this be greater than 0.
Notice that is always negative.
So for the second derivative to be positive, must also be negative (as negative times negative is positive).
.
So the values of x for which the graph is concave down are all those that are greater than .