  We make an analytic investigation of rapid quenches of relevant operators in
d-dimensional holographic CFT's, which admit a dual gravity description. We
uncover a universal scaling behaviour in the response of the system, which
depends only on the conformal dimension of the quenched operator in the
vicinity of the ultraviolet fixed point of the theory. Unless the amplitude of
the quench is scaled appropriately, the work done on a system during the quench
diverges in the limit of abrupt quenches for operators with dimension
$\frac{d}{2} \le\Delta < d$.
