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I understand how to draw this function, but what does it mean by main features? any examples for the question below?

Consider the function $f : \mathbb{R} \rightarrow \mathbb{R}$ given by $f(x) = x^2e^{-x}$.
Indicate and explain the main features?

Thanks.

amcalde
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ojando
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  • It depends on the context, but generally speaking, one might be interested in knowing things like: where is the function equal to zero; does it have maxima and minima, and if so, what and where are they; where is it increasing and where is it decreasing; what does it do as $x\rightarrow \infty$ or $x\rightarrow -\infty$; does it have any discontinuities; and so forth. If you can give some context then the question can be answered more specifically. E.g. is this a calculus course, or algebra, or what? –  Sep 11 '14 at 04:27
  • It can mean whatever the author of the problem considers as main features of the graph. Most likely: extrema, intervals of monotonicity, concavity, inflection points. –  Sep 11 '14 at 04:28
  • This is calculus or pre-calculus, not graph-theory. – Robert Israel Sep 11 '14 at 04:30
  • This was the entire question if it helps with context... Consider the function f : R -> R given by f(x) = x^2e^-x. (a) Calculate local maxima/minima and points of inflection of f(x). (b) Draw the graph of y = f(x) indicating and explaining the main features. – ojando Sep 11 '14 at 04:34

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Main features: intercepts, critical points, inflections, asymptotes, concave up/down, increasing/decreasing, symmetry.

Robert Israel
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