Section 2 looks at finding derivatives of simple functions. Section 3 introduces rates of change by looking at real life situations. Section 4 looks at using the derivative of a function to deduce useful facts for sketching its graph. Section 5 covers the second derivative test, used to determine the nature of stationary points and ends by looking at rates of change, including the real-life situation, using differentiation to find acceleration.

Course learning outcomes

After studying this course, you should be able to:

• Understand the idea of differentiation from first principles
• Differentiate power functions
• Find stationary points of some functions
• Determine the nature of some stationary points using either the first or second derivative tests
• Understand and work with derivatives as rates of change in mathematical models.