At the end of this section, students should be able to:

• Use the concept of the derivative at a point
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• Use simple rules of derivatives to find derivatives of sums and multiples of functions
• Calculate derivatives of polynomials and trigonometric functions
• Apply the chain rule in the differentiation of composite functions
• Differentiate products and quotients of simple polynomials and trigonometric functions
• Use the concept of the derivative as a rate of change
• Use the concept of stationary points
• Locate stationary points, maxima and minima, by considering sign changes of the derivative
• Calculate the second derivative,
• Interpret the significance of the sign of the second derivatives
• Use the sign of the second derivative to determine the nature of stationary points
• Obtain equations of tangents and normals to curves
• Derive the derivative of a function at a point as a limit
• Differentiate, from first principles, functions
• Use the sum, product and quotient rules for differentiation
• Differentiate sums, products, and quotients
• Apply the chain rule in the differentiation
• Composite functions (substitution)
• Functions are given by parametric equations
• Solve problems involving rates of change
• Use the sign of the derivatives to investigate where a function is increasing or decreasing
• Apply the concept of stationary (critical) points
• Calculate second derivatives
• Interpret the significance of the sign of the second derivative
• Use the sign of the second derivative to determine the nature of stationary points
• Sketch graphs of polynomials, rational functions and trigonometric functions using the features of the function and its first and second derivative (including horizontal and vertical asymptotes)
• Describe the behaviour of such graphs for large values of the independent variable
• Obtain equations of tangents and normals to curves