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Math Help - Graphing polynomial fucntions

  1. #1
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    Post Graphing polynomial fucntions

    For the function g(x)=(1-2x)^2(x-3) find
    a) the x and y intercepts
    b) the first and second derivatives,
    c)the intervals on which the function is increasing and decreasing,
    d) inflection points and concavity.
    e) finally sketch the function

    For a) I got a y intercept of (0,-3) and x-intercepts of (3,0) and (1/2,0).
    b)For the first derivative I got
    f'(x)= -4(1-2x)(x-3) + (1-2x)^2
    f''(x)= 12x^2-32x+ 13
    Can somebody please confirm whether the above two answers are correct please?

    The problem I'm having is with the question c) and d). How do I figure out what the intervals are in order to test where the function is increasing or decreasing?
    Last edited by anne25; April 27th 2012 at 07:30 PM.
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  2. #2
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    Re: Graphing polynomial fucntions

    Quote Originally Posted by anne25 View Post
    b)For the first derivative I got
    f'(x)= -4(1-2x)(x-3) + (1-2x)^2
    f''(x)= 12x^2-32x+ 13
    The first derivative is correct. Since it is a second-degree polynomial, the second derivative must be a first-degree polynomial.

    Quote Originally Posted by anne25 View Post
    The problem I'm having is with the question c) and d). How do I figure out what the intervals are in order to test where the function is increasing or decreasing?
    f(x) is increasing when f'(x) > 0 and it is decreasing when f(x) < 0. You need to solve a quadratic inequality. Similarly, f(x) is convex when f''(x) > 0 and f(x) is concave when f''(x) < 0.
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