5.1 Calculus - SL content

• 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.

• Interpret f'(x)>0, f'(x)=0 and f'(x)<0 graphically.

• Identify intervals where functions are increasing or decreasing.

• Differentiate f(x)=ax^n to f'(x)=anx^(n-1), n in Z.

• Differentiate sums of integer-power terms.

• Find tangents and normals at a given point and their equations.

• Use analytic methods and technology.

• Integrate polynomial-type functions as anti-derivatives.

• Use boundary conditions to determine constants.

• Connect anti-derivatives, definite integrals and area under curves.

• 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.

• Solve optimization problems in context.

• Examples include maximizing profit, minimizing cost and maximizing volume.

• SL examinations do not include kinematics questions.

• Approximate areas using the trapezoidal rule.

• Use equal-width intervals with a table of data or a function.