Question: A point $P(x,y)$ has a distance $5\sqrt{2}$ units from $Q(4, -7)$ and a distance $\sqrt{106}$ units from $R(-6,5)$. Knowing that, find $P$.

[the image is exactly the set of problem that our professor given to us](https://i.stack.imgur.com/hw71O.jpg)

I assume that the 3 problems are somewhat related, and the only formula that she taught us is the distance formula, which is $D =\sqrt{(x\_2−x)^2+(y\_2−y)^2}$

Answer: 
Use the epsilon-delta definition of a limit. For $h>0$ sufficiently small the difference between the fraction and the derivative at $a$ becomes arbitrarily small, hence the difference between $f(a+h)$ and $f(a)$ gets very close to $h$ times a positive constant.
$f(a)\approx h\cdot f'(a)+f(a+h)$ and $a+h$ in that neighbourhood. If $h>0$ then $f(a)<f(a+h)$ and if $h<0$ it gives $f(a+h)<f(a)$.