If \( f \phi, \psi \) are continuous in \( [a, b] \) and derivable in \( ] a, b[ \) then show th...

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If \( f \phi, \psi \) are continuous in \( [a, b] \) and derivable in \( ] a, b[ \) then show that there is a value of \( c \) lying between \( a \) and \( b \) such that,
\[
\left|\begin{array}{lll}
f(a) & f(b) & f^{\prime}(c) \\
\phi(a) & \phi(b) & \phi^{\prime}(c) \\
\psi(a) & \psi(b) & \psi^{\prime}(c)
\end{array}\right|=0
\]
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