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Math Help - Find range?

  1. #1
    Super Member fardeen_gen's Avatar
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    Find range?

    Find the range of \frac{1}{2bx - (x^2 + b^2 + \sin^2 x)}, x\in [-1,0], b\in [2,3].
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  2. #2
    Junior Member
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    Zagreb
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    Generaly:
    Bol. - Weier. theorem says: if f is continuous on [ a, b ] then f( [ a, b ] ) = [ c, d ] segment. Candidates for min and max ( c and d ) are:

    1. z = a and z = b ( f( a ) and f( b ) )

    2. f is differential in z and f ' ( z ) = 0 ( f( z ) )

    3. f is not differential in z
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  3. #3
    Super Member fardeen_gen's Avatar
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    The answer given is R_f = \left[\frac{-1}{\sin^2 (1) + 9}, \frac{-1}{16}\right]. How did we get that?
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