Assuming the conditions for the MVT hold for $\displaystyle f:\left[ {a,a + h} \right] \to $R, so that for some $\displaystyle \theta \in \left( {0,1} \right)$ we have

$\displaystyle f\left( {a + h} \right) - f\left( a \right) = hf'\left( {a + \theta h} \right)$.

If we fix f and a for each non-zero h, how would you write $\displaystyle \theta \left( h \right)$ for a corresponding value of theta?