Consider the following for the next two (02) items that follow

Let f(x) = $\left \{ \begin{matrix} x + 6, x \le 1 \\\ px + q, 1 < x < 2 \\\ 5x , x \ge 2 \end{matrix} \right.$

and f(x) is continuous 

What is the value of p ?

Consider the following for the next two (02) items that follow

Let f(x) = $\left \{ \begin{matrix} x + 6, x \le 1 \\\ px + q, 1 < x < 2 \\\ 5x , x \ge 2 \end{matrix} \right.$

and f(x) is continuous 

What is the value of q ?  

Consider the following statements :

1. f(x) = In x is increasing in (0, ∞)

2. $g(x)=e^x+e^{\frac{1}{x}} $ is decreasing in (0, ∞)

Which of the statements given above is/are correct ?  

What is the derivative of sin² x with respect to cos²x ?