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Math Help - Finding the intervals

  1. #1
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    Finding the intervals

    Find the intervals where it is increasing, decreasing, concave up, and concave down, local extreme values, and inflection points.

    y=e^x-1-x

    I took the derivative and got, e^(x-1) -1+e^(x-1)-x

    what to do next?
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  2. #2
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    intervals

    Just to clarify, is the function you have given y = e^{(x-1)} - x ?
    Last edited by nzmathman; December 1st 2008 at 08:17 PM. Reason: minor error
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  3. #3
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    Quote Originally Posted by nzmathman View Post
    Just to clarify, is the function you have given y = e^{(x-1)} - x ?
    Yes!
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  4. #4
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    If y = e^{(x-1)} - x,

    Then \frac{dy}{dx} = \frac{d}{dx} (x-1) * e^{(x-1)} - 1

    and \frac{d}{dx} (x-1) = 1

    So \frac{dy}{dx} = e^{(x-1)} - 1

    To solve for local extreme values (maxima and minima), solve \frac{dy}{dx} = 0

    To solve for where the function is increasing, solve \frac{dy}{dx} > 0

    To solve for where the function is decreasing, solve \frac{dy}{dx} < 0

    For concave up and concave down the second derivative is needed.

    \frac{d^2 y}{dx^2} = \frac{d}{dx} . \frac{dy}{dx}

    \frac{d^2 y}{dx^2} = e^{(x-1)}

    To find where the function is concave up, solve \frac{d^2 y}{dx^2} > 0

    To find where the function is concave down, solve \frac{d^2 y}{dx^2} < 0

    To find where the inflection points, solve \frac{d^2 y}{dx^2} = 0
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