Support · Mathematics Advanced 11–12 – Year 12 · Applications of calculus
Support Interpret the second derivative y'' as the gradient function of the first derivative y', and deduce that if y'' > 0 the curve is concave up and if y'' the curve is concave down
Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.
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Prerequisite dot points
Examine the gradient of a curve at a point on the curve using graphing applications
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Apply the fact that the derivative of a sum is the sum of the derivatives: d/dx(f(x) + g(x)) = f'(x) + g'(x), and the derivative of a multiple of a function is the multiple of its derivative: d/dx(k⋅f(x)) = k⋅f'(x)
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
Recognise when modelling with a non-linear function that the rate of change is not constant and is represented by the gradient of the tangent to the curve at each point on the curve
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.