Key concepts of calculus Essay Example | Topics and Well Written Essays - 500 words

Key concepts of calculus - Essay Example It is basically the instaneous rate of change of f(x) with respect to x. Graphically, this is analogous to the formula for gradient that we studied in earlier classes that is . This is basically the gradient of the tangent line to the curve traced by the function. 5. An absolute maximum value is one which is greater than all other values of f(x) for all values of x. This means there is an absolute maximum at if for all values of x. A local maximum is one which is greatest value of f(x) within a given range of x. This means 6. is basically a summation of products of countless small rectangles which form a shape on a graph. Here, is analogous to the area of a rectangle where. The only difference is that as f(x) is traced along the graph, its height changes. The number n represents the total number of rectangles made and since it approaches infinity, it means that there width grows shorter and shorter and the whole sum effectively gives the area under the curve with minimum shoot over. The main difference between definite and indefinite integral in this context is that the former has a defined domain for which this area is being calculated while the latter has domain equivalent to all real numbers. Definite integral represents area bounded by x axis, the curve and the two vertical lines at limits of domain. Indefinite integral may or may not be bounded from right or left and also, the height of curve is also unknown. So the height of rectangles is also unknown. 7. For the definite integral, bounded below by and above by , of a function, the derivative is the value of function at and the limit is the proof of its continuity. This is true regardless of the value of