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Math Help - Concavity, and inflection points! Help!

  1. #1
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    Concavity, and inflection points! Help!

    Let f(x) = x^3 + ax^2 + bx + c where a, b, and c are constants with a>0 (or a=0) and b > 0.

    a) Over what intervals is f concave up? Concave down?

    b) Show that f must have exactly one inflection point.

    c) Given that (0, -2) is the inflection point of f, compute a and c, and then show that f has no critical point.

    Really lost. All help is greatly appreciated.
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  2. #2
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    Quote Originally Posted by Hibijibi View Post
    Let f(x) = x^3 + ax^2 + bx + c where a, b, and c are constants with a>0 (or a=0) and b > 0.

    a) Over what intervals is f concave up? Concave down?
    Take the second derivative of the function and set it equal to zero. Solve for x. Test values between solutions of x. When f''(x) > 0, function is concave up. Likewise, when f''(x) < 0, function is concave down.

    Quote Originally Posted by Hibijibi View Post
    b) Show that f must have exactly one inflection point.
    Once again, solve for f''(x)=0

    Quote Originally Posted by Hibijibi View Post
    c) Given that (0, -2) is the inflection point of f, compute a and c, and then show that f has no critical point.

    Really lost. All help is greatly appreciated.
    Plug and chug my friend. How are you at finding derivatives?
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  3. #3
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    Thanks, I figured out it had to do with derivatives and was able to solve everything. I did miss the number line test though.. thanks!
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