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List of top Engineering Mathematics Questions on Mean value theorems

If a function \( f(x) \) is continuous in the closed interval \( [a, b] \) and the first derivative \( f'(x) \) exists in the open interval \( (a, b) \), then according to the Lagrange's mean value theorem:
\[ \frac{f(b) - f(a)}{b - a} = f'(c) \] If \( a = 0 \), \( b = 1.5 \), and \( f(x) = x(x - 1)(x - 2) \), then the value(s) of \( c \) in \( [a, b] \) is/are:
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