Edexcel C1 — Question 6

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
TopicDifferentiation Applications
TypeFind normal line equation
  1. The curve with equation \(y = x ^ { 2 } + 2 x\) passes through the origin, \(O\).
    1. Find an equation for the normal to the curve at \(O\).
    2. Find the coordinates of the point where the normal to the curve at \(O\) intersects the curve again.
    3. Given that
    $$y = \sqrt { x } - \frac { 4 } { \sqrt { x } }$$
  2. find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  3. find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} ^ { 2 } }\),
  4. show that $$4 x ^ { 2 } \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 4 x \frac { \mathrm {~d} y } { \mathrm {~d} x } - y = 0$$
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