anonymous
  • anonymous
Let F be the function given by f(x)= 2xe^x. Determine the interval(s) on which the graph is concave down.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Well, took find where a function concave down you know we take the second derivative and set it equal to zero to find the points of concavity. When this is done you get: 4e^x + 2xe^x = 0 Divide by the constant '2'. e^x(2+x) = 0 And while you're at it, also divide by e^x since this will never be zero. We get: x + 2 = 0 x = -2 So the intervals obtained are: (neg. infinity, -2) & (-2, pos. infinity) Substitute a value from each interval into the 2nd derivative of F, F'' = (x+2): 1. The first interval yields a negative value. 2. The second yields a positive value. So the interval that concave down is the one that yields the negative value: (negative infinity, -2)

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