14. Five marks exercise problems III

1. An open box is to be made from a square piece of material, \(24 \ cm\) on a side, by cutting equal squares from the corners and turning up the sides as shown in the below figure. Express the volume \(V\) of the box as a function of \(x\).

 

 

Volume of the box \(=\) \(4x^3 + 96x^2 + 576x\)\(4x^3 - 96x^2 + 576x\)\(4x^2 - 96x - 576\)\(4x^2 - 96x + 576\)\(4x^3 + 96x^2 - 576x\) \(cm^3\).

 

 

2. A function \(f\) is defined by \(f(x) = 3 - 2x\). Find \(x\) such that \(f(x^2) = (f(x))^2\).

 

The value of \(x\) \(=\)