IB DP Maths: AA HL复习笔记5.1.1 Introduction to Differentiation

• Before introducing a derivative, an understanding of a limit is helpful

What is a limit?

• What might I be asked about limits?

• You may be asked to use your GDC to plot the graph and use values from it to estimate a limit

What is a derivative?

• Calculus is about rates of change
  • the way a car’s position on a road changes is its speed (velocity)
  • the way the car’s speed changes is its acceleration
• The derivative is also called the gradient function

How are limits and derivatives linked?

What is the notation for derivatives?

What might I be asked about derivatives?

• From a series of gradient values, you may be asked to suggest an expression for the derivative (gradient function) of a function

What is differentiation?

• Differentiation is the process of finding an expression of the derivative (gradient function) from the expression of a function

How do I differentiate powers of x?

• How do I differentiate sums and differences of powers of x?

• What might I be asked to do once I’ve found the derivative (gradient function)?

• The derivative can be used to find the gradient of a function at any point
  • The gradient of a function at a point is equal to the gradient of the tangent to the curve at that point
  • A question may refer to the gradient of the tangent
  • A GDC can be used to help find gradients or verify answers