Q1
Answer
A curve $y=\dfrac{2\sqrt{x}-3}{x-2}$ has two stationary points.
  1. Show that the $x$ coordinates of the stationary points satisfy the equation $x - 3\sqrt{x} + 2 = 0$.
  2. Hence find the coordinates of the two stationary points.
  1. Differentiation
  2. $(1,1), (4,0.5)$
Q2
Answer
A 15 foot ladder is resting against the wall. The bottom is initially 10 m away from the wall and is being pushed towards the wall at a rate of 14 m per minute. How fast is the top of the ladder moving up the wall 12 seconds after it has started to be pushed?
$7.66$
Q3
Answer
Find the area of the finite region bounded by the curves $y=3x-x^2$ and $y=x+x^2$
$\dfrac{1}{3}$