Application of Derivatives

A fn is said to be increasing fn if f'(x) is

A fn is said to be increasing fn if f'(x) is

The equation of normal to the curve  $3x^2-y^2=8$  which is parallel to the line  $x+3y=8$  is

 $The\ function\ f\left(x\right)=\ x^2-8x+12\ is\ strictly\ decrea\sin g\ in$  

The interval in which $y=x^2e^{–x}$  is increasing is

 $The\ angle\ between\ the\ lines\ y\ =\ \sqrt{3}x\ +100\ and\ \ \sqrt{3}y\ =x\ +200\ is$  

What are the two numbers that will give the maximum product?