Support · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Support Prove by differentiation, and apply ∫uⁿdu/dxdx = 1/(n + 1)u^(n + 1) + C, where u is a function of x, or ∫f'(x)(f(x))ⁿdx = 1/(n + 1)(f(x))^(n + 1) + C, for real n≠ - 1
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Prerequisite dot points
Apply the chain rule: if y is a differentiable function of u, and u is a differentiable function of x, then dy/dx = dy/du × du/dx or if h(x) = f(g(x)) for differentiable functions f(x) and g(x) then h'(x) = f'(g(x))g'(x)
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
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Interpret piecewise-defined functions, where the function is defined differently in different parts of the domain
Mathematics Advanced 11–12 – Year 11 · Working with functions Draft mapping
No checked resources on this prerequisite dot point yet.