Can inductor voltage and capacitor current change abruptly?
but can inductor voltage and capacitor current change abruptly?


Yes, in the context of ideal circuit theory.  Indeed, this is often the case when there is a switch in the circuit.

Mathematically, if the slope of inductor current (capacitor voltage) changes abruptly, the inductor voltage (capacitor current) is discontinuous.

So, for example, consider the case that a charged capacitor, an open switch, and a resistor are in series (as in problem 2 here)

At the instant the switch is closed, the voltage across the resistor instantaneously changes from zero to the initial capacitor voltage \$V_0\$.  Thus, the capacitor current discontinuously changes from zero to non-zero and is given by

$$i_C(t) = \frac{V_0}{R}e^{-\frac{t}{RC}} \cdot u(t)$$

where \$u(t)\$ is the unit step function

The dual of this is an inductor, with non-zero current \$I_0\$, in parallel with a closed switch and a resistor.  At the instant the switch is opened, the current through the resistor changes instantly from zero to the initial inductor current.  Thus, the inductor voltage discontinuously changes from zero to non-zero and is given by

$$v_L(t) = I_0R\;e^{-\frac{tR}{L}} \cdot u(t) $$

In physical circuits, voltages and currents cannot instantaneously change but depending on the characteristic time scale, they can effectively change instantaneously.