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Curve Sketching: Solving for b and d: f(x)=x^3+bx^2+d

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data

    f(x)=x^3+bx^2+d given a critical point of (2,-4), solve for b and d

    2. Relevant equations

    f'(x)=3x^2+2bx ?

    3. The attempt at a solution

    I wasn't really sure where to go with this.

    So I know that a critical point happens when f'(x)=0, and this point can be either a max, min, or extrema.

    I tried making the derivative = to 0 and then subbed in the x value from the critical point of x=2. But i believe that this is definitely not right.

    Any help is much appreciated, thank you.
  2. jcsd
  3. Jun 11, 2012 #2


    Staff: Mentor

    From the given information, you know that f(2) = 4 and f'(2) = 0. This will give you two equations in your two unknowns so that you can solve for b and d.
  4. Jun 11, 2012 #3


    User Avatar
    Science Advisor

    No, that definitely is right! So what did you get when you put x= 2 into f'(x)= 0?
  5. Jun 11, 2012 #4
    Oh yeeesss! Thank you! I knew i would have to get two unknowns from somewhere then solve!
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