A rectangular wooden block has its volume

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Functions · Functions

Problem

A rectangular wooden block has its volume, in cubic centimetres, given by

V(x)=x^{3}-10x^{2}+31x-30,

where

x

cm is its length. The width of the block is designed to be

(x-2)

cm. (i) Determine an expression for the height of the block, in terms of

x

. (ii) If the length is fixed at

x=6

cm, calculate the exact width, height and volume of the block.