Math Help - Application of maxima and minima

1. Application of maxima and minima

Is my illustration correct? How do I start this problem? What formula do I need to use? Please consider to answer this problem because I don’t know how to start .

2. Suppose the corner is at $(0,0)$ and the end points of the log $P,Q$ are in the lines $y=8$ and $x=4$. Consider the family of lines $y=mx$ passing through $(0,0)$ . Find the points $P,Q$ and the minimum of $f(m)=d(P,Q)$.

3. please help me to continue solving this because I'm stuck her. I'm also confused in solving derivatives .thanks in advance....

4. Find the derivative of L(x)

5. i think we have to simplify first the radicand before taking the derivative