AS-Level Maths | Differentiation

• To differentiate
  • multiply the coefficient by the power
  • subtract one from the power
• To work out the x-coordinate of a stationary point
  • solve dy/dx = 0 for x
• To work out the y-coordinate of a stationary point
  • substitute x into the equation of your curve y = ...
• To work out the nature of a stationary point
  • substitute x into d²y/dx²
  • If d²y/dx² < 0 then maximum
  • If d²y/dx² > 0 then minimum
  • If d²y/dx² = 0 then check the gradient on either side
• To work out the equation of a tangent
  • use dy/dx to get the gradient
  • use equation of curve to get the y coodinate
  • y = mx + c
• To work out the equation of a normal
  • use dy/dx to get the gradient
  • take the negative reciprocal of the gradient
  • use equation of curve to get the y coodinate
  • y = mx + c

Exam questions - differentiation