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5 Calculus

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  1. 5.1 Calculus - SL content

    1. SL 5.1Limits and derivative concept

      • 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.

    2. SL 5.2Increasing and decreasing functions

      • Interpret f'(x)>0, f'(x)=0 and f'(x)<0 graphically. • Identify intervals where functions are increasing or decreasing.

    3. SL 5.3Derivative of powers

      • Differentiate f(x)=ax^n to f'(x)=anx^(n-1), n in Z. • Differentiate sums of integer-power terms.

    4. SL 5.4Tangents and normals

      • Find tangents and normals at a given point and their equations. • Use analytic methods and technology.

    5. SL 5.5Integration as anti-differentiation

      • Integrate polynomial-type functions as anti-derivatives. • Use boundary conditions to determine constants. • Connect anti-derivatives, definite integrals and area under curves.

    6. SL 5.6Stationary points

      • 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.

    7. SL 5.7Optimization

      • Solve optimization problems in context. • Examples include maximizing profit, minimizing cost and maximizing volume. • SL examinations do not include kinematics questions.

    8. SL 5.8Trapezoidal rule

      • Approximate areas using the trapezoidal rule. • Use equal-width intervals with a table of data or a function.