# Math Help - Find range?

1. ## Find range?

Find the range of $\frac{1}{2bx - (x^2 + b^2 + \sin^2 x)}$, $x\in [-1,0], b\in [2,3]$.

2. 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

3. The answer given is $R_f = \left[\frac{-1}{\sin^2 (1) + 9}, \frac{-1}{16}\right]$. How did we get that?