Question

Given y = 4x^3 -12x

Find the intervals where y is below x-axis
Find the intervals where y is above x-axis

Answer 1

Do I juz plug in random numbers and try or are there some other ways?

Answer 2

then find the roots

4x(x^2 - 3)

factorised to

\[4x(x - \sqrt{3})(x+\sqrt{3})\]


the roots exist at

\[x = -\sqrt{3} , 0. \sqrt{3}\]

below the x axis

\[x < -\sqrt{3}\] and \[0 < x < \sqrt{3}\]