# Playing Carts - I

**Calculus**Level 4

Consider a Cartesian plane where the functions \( f(x) = x^3, \; f'(x) \) and \( f''(x) \) are all plotted.

Let \(\triangle{\alpha}\) be the triangle with vertexes on all lattice points for which one of the functions intersects another.

Let \(\triangle{\beta} \) be the triangle with vertexes on the first quadrant points for which one of the functions intersects another.

Evaluate the **approximate** numerical value of the sum of \( \alpha \)'s area and perimeter plus \( \beta \)'s area and perimeter.

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.