L6FM Hwk 3 Due Mon 26.9.16

Total: 26 marks. Show all working out. Those not showing mathematical rigour will be penalised.

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1. Write in the from $a(x+b)^2 + c$
   i.e. complete the square: $$2x^2-5x-3$$

   [3 marks]

2. Simplify $$\frac{2}{x^2-3x-10} - \frac{3}{x^2-25}$$

   [4 marks]

3. Simplify as far as possible: $$\frac{15}{\sqrt {3}} - \frac{11}{2\sqrt{7} + 3\sqrt{3}}$$

   [4 marks]

4. Solve $-3-4x-5x^2>0$ showing how you arrived at your answer.

   [3 marks]

5. $$f(x)=\frac{2\sqrt x-x^2}{3x\sqrt x}$$
   1. Find the equation of the tangent at $x=4$, giving your answer in the form $ax+by+c=0$ where a,b,c are integers

      [5 marks]

   2. Find the equation of the normal at $x=4$, giving your answer in the form $ax+by+c=0$ where a,b,c are integers

      [4 marks]

   3. Find $f''(4)$

      [3 marks]