Calculus
posted by Anonymous .
Function f(x)= e^x^2
a) Inflection Values
b) Intervals on which f(x) is concave downward
c) Intervals on which f(x) is concave upward.

If 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^21)
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?
Respond to this Question
Similar Questions

Calculus
Suppose you know that f(x) is an odd functon on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5. List ALL intervals on … 
calculus
Let f (x) = x^2 + 5x14. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection … 
calculus
Let f (x) = x3 ��3x2 +5x+2. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f . 1. f is concave up on the intervals 2. f is concave down on the intervals … 
calculus
Let f (x) =7x5/x+3 . Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f . 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection … 
calculus
let f(x) = 2x^55x^4 find open intervals on which f is a) increasing b)decreasing Find values of x at which f has c) relative max and min find open intervals d) concave upward e) concave downward c) find the inflection points of f 
Calculus
THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on which the function is concave up or concave down. I finally understand that when f'' is greater than 0 it means concave up. f(X) = 18x^2 + x^4 so I differentiate that … 
calculus
If f(x) = 3 cos^2(x) − 6 sin(x) 0 ≤ x ≤ 2π Find the intervals of increase and decrease, the intervals of concave up and concave down, local maximum values, local minimum values, and inflection point 
Calculus
Consider the function f(x)=(x^2)e^(14x) f(x) has two inflection values at x = C and x = D with C≤D where C is and D is Finally for each of the following intervals, tell whether f(x) is concave up or concave down. (−∞,C]: … 
Calculus
f(x)= x/(1+x)^2 c) find the intervals of concavity and the inflection points. My answers: f is concave downward on ( infinity, 2) and concave upward on (2, infinity). Inflection point: ( 2, 2/9) 
Calculus
Let f(x)=−x^4−8^x3+5^x+2. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals …