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Calculus

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For what values of x does the graph of F9x) = 2x^3 - 3x^2 + 12x + 87 have a horizontal tangent?

  • Calculus -

    this is the same as asking where F'(x) = 0

    Since F'(x) = 6x^2-6x+12

    where would that be?

  • Calculus -

    6x4=24
    2x6=12+12=24

    so...2?

  • Calculus -

    No, it's almost a trick question.
    6x^2-6x+12 is never zero (has no real roots)

    So, F(x) never has a horizontal tangent.
    Visit wolframalpha.com and type in

    2x^3 - 3x^2 + 12x + 87

    and it will show the graph and various properties of the function. You will be able to see clearly that there is no horizontal tangent.

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