[填空题]
Olivia designs a logo for a mountain campqqixr8;ys8 q* 2 ivci;ing club. The logo is i(znnqqe i/ q6;8pbu+u n the shape of a right-angled triangle, ABC, which represents a mountain. A rectangular sectiuq ;p8 z qn/n+q6iube(on, ADEF, is inscribed inside the triangle to create a view of two smaller mountains. The lengths of BD, DE, EF and FC are p cm, 4 cm, 6 cm and q cm respectively.
The total area of the logo is $A \mathrm{~cm}^{2}$ .
1. 1. Find A in terms of p and q , giving your answer in the form A=a p+b q+c ;A=ap+bq+c;a= ,b= ,c= .
2. Show that A=$\frac{48}{q}+3q+24$ .
2. Find $\frac{\mathrm{d} A}{\mathrm{~d} q}$=-$\frac{a}{q^b}$+c；a= ,b= ,c= .
Olivia wishes to find the value of q that will minimize the area of the club logo.
3. 1. Write down an equation Olivia could solve to find this value of q .
2. Hence, or otherwise, find this value of q = .
