A natural cubic spline for a function f$($x$)$ is defined byS$($x$)=$a$1$x$^3+15$x$^2-21\mathrm{.}75$x xS$($x$)=$a$2$x$^3+3$x$^2+2\mathrm{.}25$xxFind the value of a$2.$

A natural cubic spline for a function $f(x)$ is defined by

$S(x)=\{[a_1{x}^3+15x^2-21\mathrm{.}75x+14\mathrm{.}5,1x2],[a_2{x}^3+3x^2+2\mathrm{.}25x-1\mathrm{.}5,2x3]\}$

Find the value of $a_2.$