differentiation

Question 1

possible questions

Answer 1

• differentiation
• rate of change
• stationary points
• equation of a tangent
• closed intervals
• sketching a graph
• optimisation
• further differentiation
• differentiating sin and cos

Question 2

differentiation rules

Answer 2

• no x on bottom
• no root sign
• no brackets

Question 3

rate of change process

Answer 3

• differentiate
• sub into x

Question 4

stationary points process

Answer 4

• differentiate
• SPs occur when f(x)=0
• factorise
• nature table
• max and min TP

Question 5

sketch a graph process

Answer 5

• 5 step programme
• roots (factorise)
• y-intercept (sub 0 into x)
• check what happens at ends (sub in positive and negative to x)
• sketch graph

Question 6

equation of a tangent process

Answer 6

• gradient (by differentiating)
• find y (sub x into original)
• equation

Question 7

closed intervals process

Answer 7

• 5 step programme
• check edges of domain (sub domain into original to find y)

Question 8

further differentiation steps

Answer 8

• f(x)= (4x²-3)⁻⁸
  ‎
• f¹(x)= -8(4x²-3)⁻⁹x 8x
• =-64x(4x²-3)⁻⁹

Question 9

differentiating sin and cos steps

Answer 9

• f(x)= 6cos³x
  ‎
• f¹(x)= 18(cosx)²x-sinx
• = -18sinxcos²x