Calculus

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Determine the maximum and minimum value of the function f(x)=-xe^x + 2.

  • Calculus -

    Forget the calculus, sketch a graph.

  • Calculus -

    -10 2.0005
    -3 2.14
    -2 2.27
    -1 2.4 maximum
    -0.5 2.3
    0 2
    1 -.72
    2 -12.8
    10 -220,263 minimum as x -->oo

    derivative
    y' = -[ xe^x + e^x]
    = -e^x [x+1]
    so max or min at x = -1
    second derivative
    y" = - [e^x(1)+(x+1)e^x]
    = -e^x [ x+2 ]
    if x = -1
    then = -(1/e)(1)
    negative so maximum

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