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March 28, 2017

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What is the point of inflection of the function f(x)=x^3-8x^2+5x+50? Is the local extrema at f(1/3)=50.8 max and f(5)=0 min?

For the second derivative I got f(x)=6x-16 and then got x=16/6 when set to zero.

  • Calculus - ,

    3 x^2 -16 x + 5 = 0
    first derivative
    at x = {16 +/-sqrt(256-60)]/6
    or [16+/-14]/6 = 5 or 0.3333

    second derivative
    6 x - 16
    is that + or - at the two points where the slope is zero?
    at x = .333
    2 - 16 is negative so maximum there
    at x = 5
    6x - 16 = 30-16 is positive so minimum there

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