Topic 4: Applications of differential calculus — Maths Interactives

Graphical applications of derivatives

12 hours

Determine instantaneous rates of change.
Determine the equation of a tangent and a normal of the graph of 𝑦 = 𝑓(𝑥).
Construct and interpret displacement-time graphs, with velocity as the slope of the tangent. 1 interactive
Recognise that velocity is the instantaneous rate of change of displacement with respect to time.
Use the first derivative of a function to determine and identify the nature of stationary points. 1 interactive
Sketch curves associated with power functions and polynomials up to degree 4; find stationary points and local and global maxima and minima with and without technology; and examine behaviour as 𝑥 → ∞ and 𝑥 → − ∞.