Applying Differentiation to Problems in Context

Applying Differentiation to Problems in Context

Understanding the Context

  • Know that differentiation is a powerful mathematical tool that has numerous practical applications.
  • Recognise that real-world problems often involve rates of change, which can be modelled using calculus and differentiation.
  • Be aware that the ‘context’ can imply situations from various fields like physics, economics, biology and more.

Contextualising Differentiable Functions

  • Learn to interpret problems in context and model them using differentiable functions.
  • Understand how to represent various aspects of real-world scenarios using mathematical language.
  • Be clear on the key mathematical features of a real-world problem and how they translate into mathematical expressions.

Methods for Differentiation in Context

  • Appreciate the different methods for differentiation and their appropriate use depending on the problem in hand.
  • Get comfortable with the power rule, product rule, quotient rule, and chain rule.
  • Keep in mind that you may have to use combinations of these rules in complex contextual situations.

Sections in Contextual Problems

  • Be able to identify the quantities that change and stay the same in a given context.
  • Familiarise yourself with formally establishing what constitutes the ‘rate of change’ in a problem.
  • Master how to find derivatives in these contexts and interpret what these derivatives mean.

Solving Contextual Problems

  • Practice taking word problems or given situations and translating them into mathematical problems involving differentiation.
  • Evaluate your answers to ensure they align logically with the given context, making sure to express your answer in units that make sense.
  • Regularly solve a range of contextual problems to deepen your understanding of how differentiation is applied in real life situations.

Mistakes to Avoid

  • Avoid the common mistake of overlooking what the derivative actually means in the given context.
  • Do not forget to include appropriate units in your final answers.
  • Remember to correctly interpret the question sort, not to incorrectly use negative signs especially when dealing with physics problems involving motion.