The values of 'a' and 'b' such that the function defined by is a continuous function: $ f(x)=\left\{\begin{array}{cc} 3 & x \leq 5 \\ a x+b & 5<x \leq 15 \\ 18 & x>15 \end{array}\right. $

$a=2, b=1$ $a=\frac{3}{2}, b=\frac{-9}{2}$ $a=\frac{3}{2}, b=\frac{9}{2}$ $a=\frac{-3}{2}, b=\frac{9}{2}$

$a=\frac{3}{2}, b=\frac{-9}{2}$

The correct answer is Option (2) → $a=\frac{3}{2}, b=\frac{-9}{2}$