Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Estimate limits from tables or graphs; formal analytic limit methods are not required. • Interpret derivative as gradient function and rate of change. • Use notation dy/dx, f'(x), dV/dr and ds/dt.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Interpret f'(x)>0, f'(x)=0 and f'(x)<0 graphically. • Identify intervals where functions are increasing or decreasing.
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Learning objective
• Differentiate f(x)=ax^n to f'(x)=anx^(n-1), n in Z. • Differentiate sums of integer-power terms.
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Learning objective
• Find tangents and normals at a given point and their equations. • Use analytic methods and technology.
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Learning objective
• Integrate polynomial-type functions as anti-derivatives. • Use boundary conditions to determine constants. • Connect anti-derivatives, definite integrals and area under curves.
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Learning objective
• Find x-values where gradient is zero by solving f'(x)=0. • Use technology to generate f'(x) and find local maxima/minima. • Local extrema may not be absolute extrema on a domain.
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Learning objective
• Solve optimization problems in context. • Examples include maximizing profit, minimizing cost and maximizing volume. • SL examinations do not include kinematics questions.
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Learning objective
• Approximate areas using the trapezoidal rule. • Use equal-width intervals with a table of data or a function.
Start with the concept explanation, then practise to create mastery evidence.