1 answer

6. For € (-1, +00) consider the function f(x) = x'e- (a) (6 points) Find (if...

Question:

6. For € (-1, +00) consider the function f(x) = xe- (a) (6 points) Find (if any; note that limz++oc f(x) = 0): • local maxim

6. For € (-1, +00) consider the function f(x) = x'e- (a) (6 points) Find (if any; note that limz++oc f(x) = 0): • local maxima: • localminima: • global maximum: • global minimum: (b) EXTRA CREDIT (1 point): define what is an INFLECTION POINT (and, if you wish, draw a picture illustrating it); (c) (4 points) find the inflection points of f() (if any); (d) EXTRA CREDIT (4 points): sketch the graph of f (recall that limz++00 f(x) = 0).

Answers

Application of Derivative: Given, f(x)=xe-* xe[-1…] Find (if any note that lim f(x)=0) We have to find that local and globalNow find the value of second derivative of function at the critical point as follows: f (x) = (2–2x)e** - (2x - x)e* =e* (2-Now find the value of the function at this critical point and end point of the given interval. x x=0 f(x) f(0) = 0 4 x=2 f(2)(b) Inflection point is a point where second derivative is zero or undefined and it is also defined as the point where graph(d) Sketch of Graph: 2 0 00 00 N

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