Posted by **Janet** on Sunday, April 17, 2011 at 1:15am.

let f(x)=x^3(e^-x)

Answer using calculus, use graphing calculator only to check work.

a) Find the local and global extrema of f.

b) Find the intervals where f is increasing/decreasing.

c) Find the inflection points of f.

d) Find the intervals where f is concave up/down.

e) Find any asymptotic behavior (use limits to justify your answer)

Here's my work. Not sure I did it right so if someone could check. I don't know how to do e).

f'(x) = x^2(e^-x)(-x+3)=0

critical values are x=0 and x=3.

Not sure how to use these values to find part a.

f"(x)= x(e^-x)(-6x+x^2+6)

x=0, x=4.7321, x=1.2679 (find these with quadratic equation). These are the inflection points.

Increasing for x<3, until it hits x=3 which I think is the maximum (not sure if it's local or global extrema).

Decreasing for x>3, hit a local minimum at x=0 ( I'm not sure on these parts)

Concave up (0,1.2679), (4.7321, infinity)

Concave down (-infinity,0), (1.2679,4.7321)

I don't know how to do part e.

## Answer This Question

## Related Questions

- Math - For y= (3x)/(2e^x+e^-1), use graphing techniques to find the approximate ...
- Calculus - For y=(1/4)x^4-(2/3)x^3+(1/2)x^2-3, find the exact intervals on which...
- Calculus (urgent!!) - Please answer the following questions about the function f...
- Calculus (pleas help!!!) - Please answer the following questions about the ...
- Calculus (pleas help!!!) - Please answer the following questions about the ...
- calculus I - hi! can someone please help me ... question: a)find the intervals ...
- Calculus - Use any calculus method to determine extrema, intervals where the ...
- Calculus.......plz help! =) - Use any calculus method to determine extrema, ...
- Calculus - a) find the intervals on which f is increasing or decreasing. Is it...
- Calculus - f(x)= x/(1+x)^2 a) find the intervals on which f is increasing or ...

More Related Questions