Is f(x)=x12sin(3xπ4) increasing or decreasing at x=π6?

1 Answer
Dec 1, 2015

It's decreasing.

Explanation:

The answer lies in the first derivative: if it is positive at x=π6, the function will be increasing, otherwise it will be decreasing.

So, the first derivative is

112cos(3xπ4)3=136cos(3xπ4)

Evaluate at x=π6:

136cos(3(π6)π4)=136cos(π2π4)
=136cos(π4)=13622
=1182

which is clearly negative. So, the function is decreasing, as you can see in the graph.