What you’ll learn8 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—SL 5.1—Limits 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.Syllabus objective—SL 5.2—Increasing and decreasing functions• Interpret f'(x)>0, f'(x)=0 and f'(x)<0 graphically.• Identify intervals where functions are increasing or decreasing.Syllabus objective—SL 5.3—Derivative of powers• Differentiate f(x)=ax^n to f'(x)=anx^(n-1), n in Z.• Differentiate sums of integer-power terms.Syllabus objective—SL 5.4—Tangents and normals• Find tangents and normals at a given point and their equations.• Use analytic methods and technology.Syllabus objective—SL 5.5—Integration 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.Syllabus objective—SL 5.6—Stationary 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.Syllabus objective—SL 5.7—Optimization• Solve optimization problems in context.• Examples include maximizing profit, minimizing cost and maximizing volume.• SL examinations do not include kinematics questions.Syllabus objective—SL 5.8—Trapezoidal rule• Approximate areas using the trapezoidal rule.• Use equal-width intervals with a table of data or a function.Syllabus objective