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Math Help - Not sure how to do this one

  1. #1
    Junior Member NAPA55's Avatar
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    Not sure how to do this one

    Use calculus techniques (can they be a bit more specific? ) to show that the graph of the quadratic function f(x) = ax2 + bx + c, a>0 is decreasing on the interval x<(-b/2a) and increasing on the interval x>(-b/2a).
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by NAPA55 View Post
    Use calculus techniques (can they be a bit more specific? ) to show that the graph of the quadratic function f(x) = ax2 + bx + c, a>0 is decreasing on the interval x<(-b/2a) and increasing on the interval x>(-b/2a).
    well lets start with what we know and some calculus.

    f(x)=ax^2+bx+c let take the derivative

    f'(x)=2ax+b set the derivative equal to zero.

    2ax+b=0 \iff x=-\frac{b}{2a} this is the critical point

    now taking the 2nd derivative we get

    f''(x)=a \mbox{ but } a > 0 so the graph is concave up

    so the graph is decreasing on (\infty,-\frac{b}{2a})

    and increasing on (-\frac{b}{2a},\infty)
    Last edited by TheEmptySet; April 20th 2008 at 06:24 PM. Reason: typo
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by NAPA55 View Post
    Use calculus techniques (can they be a bit more specific? ) to show that the graph of the quadratic function f(x) = ax2 + bx + c, a>0 is decreasing on the interval x<(-b/2a) and increasing on the interval x>(-b/2a).
    Uhm...you posted a question like EXACTLY like this like 3 weeks ago...if you need further guidance refer back to that post
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