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Sketching graphs Calculus


paperpheasant

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I have a question specifically about Math SL calculus part-

do we have to know how to sketch the graph of function basing on the first and second derivative, like the points of inflection, local and global maxima/minima, or vertical tangents and cusps.?

or is it just enough to draw it with the aid of GDC.?

I mean, can specifically sketching a function with those derivatives and all features can happen on paper 1.?

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I know that for maths HL you had to know how to do this, and you'd quite regularly get questions asking you to sketch the derivative/antiderivative of a function by looking at a sketch of the function (and sometimes its derivative). Looking at the maths SL syllabus, there's no direct mention of sketching graphs, but it definitely seems that you need to understand the theory behind it, so perhaps you could get a question about it. They say that you need to know:

Graphical behaviour of functions: tangents and normals, behaviour for large x, horizontal and vertical asymptotes.

The significance of the second derivative; distinction between maximum and minimum points.

Points of inflexion with zero and non-zero gradients.

Both “global” and “local” behaviour.

Use of the terms “concave-up” for f ′′(x) > 0 , “concave-down” for f ′′(x) < 0 .

At a point of inflexion f ′′(x) = 0 and f ′′(x) changes sign (concavity change). f ′′(x) = 0 is not a sufficient condition for a point of inflexion: for example, y = x4 at (0,0) .

http://www.education.umd.edu/MathEd/conference/vbook/math.sl.08.pdf

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