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Use the Intermediate Value Theorem to check whether the equation x^3–3x+2.1=0 has a root in the interval (0,1)
answer: yes or no ?

i have no idea how to answer to go about solving this question, thanks for the help!

  • Calc -

    if x = 0 the function is 2.1
    if x = 1 , the function is 0.1
    so it does not necessarily cross the x axis between those points

    If it does cross, it must cross twice to go from + to - to + again
    so it would have to have a slope of zero in between there
    df/dx = 3 x^2 -3
    0 = x^2 - 1
    x= +1 or -1 for 0 slope
    so it has no zero slope points between 0 and 1
    It never crosses the x axis between 0 and 1

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