IB DP Maths: AI 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?What is a derivative?

How are limits and derivatives linked?

What is the notation for derivatives?

What might I be asked about derivatives?

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?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