1. x-intercepts

when x = 0, x = -√6 and x = √6

2. y-intercepts:

When x = 0, y = 0.

3. maxima and minima?

Now dy/dx = 0 when x = 0 or x = -√3 or x = √3

So we have max or min at (0,0) and (-√3,-9) and (√3,-9).

4. Second derivative:

Now y" > 0 for x = -√3 so (-√3, -9) is a local MIN

Now y" < 0 for x = 0 so (0, 0) is a local MAX

Now y" > 0 for x = √3 so (√3, -9) is a local MIN

We now use the second derivative to find points of inflection:

when x = -1 or x = 1

If x < -1, y" > 0, and for -1 < x < 1, we have y" < 0.

So the sign of y" has changed, so (-1, -5) is a point of inflection.

If x > -1, y" > 0,

So the sign of y" has changed, so (1, -5) is a point of inflection.

So we are ready to sketch the curve: