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March 29, 2017

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use mean value theorem:
f(x)= 7- 2^x, [0,4], c=?

  • Calculus - ,

    f(4) = -9
    f(0) = 6
    so, we want f'(c) = -15/4

    f'(x) = -ln2 2^x
    -15/4 = -ln2 2^c
    15/(4ln2) = 2^c
    ln(15/ln16) = c ln2
    c = ln(15/(4ln2))/ln2 = 2.4356

    which is in the interval [0,4]

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