Is there any software which can plot the graph of any function provide

[ritwik06]

When the first derivative is 0, then those corresponding points represent the maxima or minima. Is it always true? What r points of inflexion? And why is the derivative 0 there? At which other points is the derivative 0?


Is there any software which can plot the graph of any function provided to it as input?

regards,
Ritwik

 

[CompuChip]

What is the derivative of a function? What does it mean "geometrically" (as in: relating to the graph of the function) when the derivative is 0 in a point?

Points of inflection are those points where the derivative vanishes, but there is not a minimum or a maximum (for example, the point x = 0 for the graph x³).

Finally, yes, such software exists (Mathematica, MatLab, Maple) which can plot functions in up to 3 dimensions, but is usually very expensive. You could check at your school / university / ... if they have it installed or available for students to take. But if you Google for "function grapher" or something like that, you will probably find a lot of simple ones already (http://people.hofstra.edu/steven_r_costenoble/Graf/Graf.html, for example).

 

[HallsofIvy]

Points of inflection are those points where the derivative vanishes, but there is not a minimum or a maximum (for example, the point x = 0 for the graph x³).

This is incorrect. A "point of inflection" is a point where the second derivative changes sign. It is not necessary that the derivative be 0 there. As long as the function is twice differentiable, it is necessary that the second derivative be 0 there.

 

[CompuChip]

Ah, you're right. I thought that "point of inflection" was synonymous with "saddle point", but the latter is just a special case. Sorry for the confusion.