Plot a the function is discontinuous at x 1, because ln 1 0. A full lesson on sketching cubics, quartics and reciprocal functions. Detailed example of curve sketching x example sketch the graph of fx. While you may not be tested on your artistic ability to sketch a curve on the ap calculus exams, you will be expected to determine these specific features of graphs. A worked solution to a past paper question taken from aqa fp1. Mathematics learning centre, university of sydney 1 1 curve sketching using calculus 1. Show that, if a 1, then c has exactly one stationary point. Detailed example of curve sketching mit opencourseware. This topic has been discussed under quadratics and polynomials in core 1, and under curve sketching in core 2. This is a fancy title referring to curve sketching with the help of calculus.
Curve sketching practice questions above handout 5. Mathematics revision guides more curve sketching page 2 of 23 author. For many students, one of the first hard calculus topics that make them realise the real deal is on for their hsc 2 unit maths year is the geometry of the derivative. Incorporates the use of geogebra and the casio fx991ex classwiz. Use the number line to determine where y is increasing or decreasing. Veitch 1 p x 1 0 1 p x 1 1 p x 1 x the other critical value is at x 1. This calculus video tutorial provides a summary of the techniques of curve sketching. In this article, youll see a list of the 10 key characteristics that describe a graph. The sketch must include the coordinates of all the points where the curve meets the coordinate axes. Find the domain of the function and determine the points of discontinuity if any. Further maths asymptotes and curve sketching youtube. The ten steps of curve sketching each require a specific tool. The following steps are taken in the process of curve sketching.
Although this is not a wjec question, the skills are very relevant to wjec fp2. This covered the methods of sketching other types of functions, such as cubics or reciprocals. Step support programme step ii curve sketching questions. Based on the graph of f x, shown to the right, which of the. This handout contains three curve sketching problems worked out completely.