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Math Help - Hi i need help with a two part function and symmetry problem

  1. #1
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    Hi i need help with a two part function and symmetry problem

    Hi, i have a two part symmetry and function related question:
    A. Find the point of symmetry of the graph of the cubic function:
    f(x)=-x^3+15x^2-48x+45

    B. The function has a local minimum at (2,1). At what point does a local maximum occur?
    I don't understand how to go about this problem.. can anyone help?
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  2. #2
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    Quote Originally Posted by mathstudent123 View Post
    Hi, i have a two part symmetry and function related question:
    A. Find the point of symmetry of the graph of the cubic function:
    f(x)=-x^3+15x^2-48x+45

    B. The function has a local minimum at (2,1). At what point does a local maximum occur?
    I don't understand how to go about this problem.. can anyone help?
    1. With a cubic function the point of symmetry is the inflection point. Therefore solve for x:

    f''(x) = 0

    2. The point of symmetry is the midpoint between 2 corresponding points of the graph. If the point of symmetry is S(5, 55) and the maximum point is M(a, b) then

    \dfrac{2+a}2 = 5~\wedge~\dfrac{1+b}2=55
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