OCR C2 — Question 9

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
TopicDifferentiation Applications
TypeFind tangent line equation

9. The curve \(C\) has the equation \(y = \mathrm { f } ( x )\) where $$f ^ { \prime } ( x ) = 1 + \frac { 2 } { \sqrt { x } } , \quad x > 0$$ The straight line \(l\) has the equation \(y = 2 x - 1\) and is a tangent to \(C\) at the point \(P\).
  1. State the gradient of \(C\) at \(P\).
  2. Find the \(x\)-coordinate of \(P\).
  3. Find an equation for \(C\).
  4. Show that \(C\) crosses the \(x\)-axis at the point \(( 1,0 )\) and at no other point.