![]() ![]() The formulae on the formula page are restricted to the formula for determining the gradient/derivative of a function at a point using first/basic principles and the average gradient formula: 0 2 1 2 1 ( ) () () lim h fx h fx f x h y y Ave m x x Students and teachers are reminded that all area (total surface area), perimeter and volume formulae for prisms, spheres, pyramids and hemispheres are not necessarily given – any of these formulae is applicable in calculus when determining the maximum/minimum volume or area. Calculating the limit of the average gradient as the time tends to zero, leads us to the derivative at a certain time, which is nothing else than the velocity at a certain time. This topic will be made clear if we look at the average gradient of a distance time graph, namely distance divide by time (m/s). Students must understand why the derivative of the distance with respect to time gives the speed/velocity at a specific time and the derivative of the speed gives the acceleration at a specific time. ![]() Linking calculus with motion, distance, speed and acceleration is highlighted. The link between gradient at a point and the derivative is important as it is the reasons behind taking the derivative and setting it equal to zero to determine the maximum/minimum volume, area or distance. The next emphasis is put on average gradient (average rate of change) in comparison to determining the gradient at a point or the rate of change at a certain value. Hence the first five videos give an in depth look at the reasons why calculus was developed. It is important for students to be made aware of the uses of calculus over the wide spread of subjects and to get to grips with the ultimate application of calculus. A Guide to Differential Calculus Teaching Approach Calculus forms an integral part of the Mathematics Grade 12 syllabus and its applications in everyday life is widespread and important in every aspect, from being able to determine the maximum expansion and contraction of bridges to determining the maximum volume or maximum area given a function.
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