Wednesday

October 22, 2014

October 22, 2014

Posted by **Anonymous** on Tuesday, March 29, 2011 at 12:14am.

a) Inflection Values

b) Intervals on which f(x) is concave downward

c) Intervals on which f(x) is concave upward.

- Calculus -
**Reiny**, Tuesday, March 29, 2011 at 8:44amIf you look at the graph of this function you will see a standard "bell curve"

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

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

= 4x^2(e^(-x^2)) - 2(e^(-x^2))

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

(e^(-x^2)) = 0

1/(e^(x^2))= 0 -----> no solution

or

2x^2 - 1 = 0

x = ± 1/√2

sub that back into f''(x) to find the values at the points of inflection

b) f(x) is concave down when f''(x) < 0

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

clearly (e^(-x^2)) or 1/(e^(x^2)) is always positive, so all we need to look at is the 2x^2 -1 part

concave up for -1/√2 < x < 1/√2

c) mmmmhhh?

**Answer this Question**

**Related Questions**

calculus - let f(x) = 2x^5-5x^4 find open intervals on which f is a) increasing...

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 - Suppose you know that f(x) is an odd functon on the domain of all ...

Calculus - THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on ...

calculus - Please help me solve. I think increase = concave up and decrease = ...

grade 12 AP calculus - for f(x= -1/4x4-1/3x3+2x, use analytic method to find the...

Calculus - f(x)=[3x^13]e^(−7x) On which intervals is the function concave ...

Math ( calculas) - find the intervals on which the curve y=x/(x+1)^2 is concave ...