While JEE Main focuses on single-variable MVT, understanding the extension provides deeper insight:

For f: R -> R (single variable): f(b) - f(a) = f'(c)(b-a) — LMVT.

For f: $R^n$ -> R (multivariable): f(b) - f(a) = grad(f)(c) . (b-a) for some c on the line segment from a to b.

Why this matters for JEE: Multivariable MVT is NOT tested, but the intuition carries over: the rate of change along any direction must equal the average rate of change at some point.