Support · Mathematics Advanced 11–12 – Year 12 · Applications of calculus
Support Use differentiation to find and interpret the first and second derivatives, dQ/dt and (d²Q)/(dt²), in practical problems where a quantity Q is a function of time t
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
Use first principles to find the derivative of quadratic functions
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
Identify stationary points on the graph of a cubic function, and the values of x for which the function is increasing and/or decreasing, by first calculating the derivative, and justify conclusions
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
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.