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 $x$ $=$