Calculus

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Find constants a,b and c such that the graph of f(x)=x^3+ax^2+bx+c will increase to the point (-3,18), decrease to the point (1,-14) and then continue increasing.

  • Calculus -

    Find constants a,b and c such that the graph of f(x)=x^3+ax^2+bx+c will increase to the point (-3,18), decrease to the point (1,-14) and then continue increasing.
    ==============================
    The derivative is zero at x = -3 and x = 1
    f' = 3 x^2 + 2ax + b
    0 = 3(9) +2a(-3) +b = 27-6a+b
    and
    0 = 3(1) +2a(1) +b = 3 +2a+b
    so solve those two equations for a and b
    then use the value of y = -1 at x = 1 to get c

  • Calculus -

    Thank you Damon, but I still do not understand.

    How do I solve for a, if I rearrange 27-6a+b in terms of a, I get a= 27+b/6.
    But what do I plug in for b?

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