SOLUTION: Find the x-coordinates of the local max and local min points of f(x)=x^2e^x+5

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Question 1026208: Find the x-coordinates of the local max and local min points of f(x)=x^2e^x+5
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%5E2e%5Ex%2B5 ==> y' = %28x%5E2%2B2x%29e%5Ex ==> y" = %28x%5E2+%2B4x+%2B2%29e%5Ex (Verify!!)
y' = 0 ==> x = 0, -2
Use the 2nd derivative test:
At x = 0: y" = %280%5E2+%2B4%2A0+%2B2%29e%5E0+=+2+%3E+0 ==> local min at x = 0.
At x = -2: y" = %28%28-2%29%5E2+%2B4%2A%28-2%29+%2B2%29e%5E%28-2%29+=+-2%2Fe%5E2+%3C+0+==> local max at x = -2.