Posted by **anonymous** on Saturday, April 20, 2013 at 9:42pm.

Consider the function f(x)=xe^2x. Find the intervals on which f(x) is concave up and the intervals where it is concave down. Show a sign graph.

Please show work in detail so I can follow for future reference. Thanks!

- Calculus -
**Reiny**, Saturday, April 20, 2013 at 10:33pm
The curve is concave up if f '' (x) is positive and

concave down if f '' (x) is negative

f ' (x) = x(2)e^(2x) + e^(2x)

= e^(2x) (2x + 1)

f '' (x) = (2x+1)(2)e^(2x) + 2 e^(2x)

= 2 e^(2x) ((2x+1) + 1)

= 2 e^(2x) (2x + 2)

= 4 e^(2x) (x+1)

since 4e^(2x) > 0 for all values of x, we just have to look at

x + 1

x+1 > 0 for x > -1

x+1 < 0 for x < -1

so the curve is concave up for all values of x > -1

and concave down for all values of x < -1

check the graph by Wolfram

http://www.wolframalpha.com/input/?i=plot+x+e%5E%282x%29%2C+-3+%3C+x+%3C+1+%2C+-.25+%3C+y+%3C+2

notice there is a point of inflection at x= -1

## Answer This Question

## Related Questions

- Calculus - THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on ...
- Calculus - Suppose you know that f(x) is an odd functon on the domain of all ...
- calculus - Let f (x) = x3 ��3x2 +5x+2. Find the open intervals on ...
- calculus - Let f (x) =7x-5/x+3 . Find the open intervals on which f is concave ...
- calculus - Let f (x) = x^2 + 5x-14. Find the open intervals on which f is ...
- Calculus - Find the intervals where the function f(x)=((2x-1)^2)(x-3)^2 is ...
- calculus - Please help me solve. I think increase = concave up and decrease = ...
- Calculus - f(x)=[3x^13]e^(−7x) On which intervals is the function concave ...
- Calculus - Let f(x)=−x^4−8^x3+5^x+2. Find the open intervals on ...
- math-calc - Consider the function f(x)= (2x+8)/(6x+3). For this function there ...

More Related Questions