Question

At what intervals is y=x^4-6x^2 increasing and concave down

Answer 1

First find the general shape of \(f(x)=x^4-6x^2\) as \(x=\pm \infty\).
Since the leading coefficient is positive, and the degree is 4, we conclude that the general shape is like a W, concave up.

Answer 2

The part which is concave down would be delimited by two inflection points A,B obtained by equating f"(x)=0.

Answer 3

The part increasing would be between A and the local maximum C which can be found readily by equating f'(x)=0 or even by inspection.