Wednesday 21 September 2016

L6FM Hwk 3 Due Mon 26.9.16

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

PRINT OUT FOR YOUR RECORDS

  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]

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