Let \(f:\left[1,∞\right)\to ℝ\) be a differentiable function. If \(6{\int }_{1}^{x}f\left(t\right)dt=3xf\left(x\right)+{…

Let \(f:\left[1,∞\right)\to ℝ\) be a differentiable function. If \(6{\int }_{1}^{x}f\left(t\right)dt=3xf\left(x\right)+{x}^{3}−4\) for all \(x\geq 1\), then the value of \(f(2)–f(3)\) is

[JEE Main 2026, 22 Jan (Shift 1)]