SOLUTION: Please help me solve this problem: 1. Determine the intervals of increase and decrease of y=2e^(-5x^2) 2. Where is the curve of the graph y=2e^(-5x^2) concave upward and downw

Algebra ->  Test  -> Lessons -> SOLUTION: Please help me solve this problem: 1. Determine the intervals of increase and decrease of y=2e^(-5x^2) 2. Where is the curve of the graph y=2e^(-5x^2) concave upward and downw      Log On


   

Question 1014991: Please help me solve this problem:
1. Determine the intervals of increase and decrease of y=2e^(-5x^2)
2. Where is the curve of the graph y=2e^(-5x^2) concave upward and downward?
Thank-you, your help is always appreciated!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Differentiate.
df%2Fdx=-20x%2Ae%5E%28-5x%5E2%29
Since the second term is always positive, the sign of the derivative is determined by the value of x.
Positive (increasing) when x%3C0, negative (decreasing) when x%3E0.
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Differentiate again,
d%28df%2Fdx%29%2Fdx=20%2810x%5E2-1%29%2Ae%5E%28-5x%5E2%29
Again the second term is always positive.
The quadratic term determines the sign of the second derivative.
10x%5E2-1=0
10x%5E2=1
x%5E2=1%2F10
x=0+%2B-+sqrt%2810%29%2F10
So the function is concave up (-infinity,-sqrt%2810%29%2F10), concave down from (-sqrt%2810%29%2F10,sqrt%2810%29%2F10), and concave up from (sqrt%2810%29%2F10,infinity).
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