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.
$

$a=\frac{3}{2}, b=\frac{-9}{2}$

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

$f(5)=3$

$\lim\limits_{x→5^+}ax+b=5a+b=3$  ...(1)

$f(15)=18$

$\lim\limits_{x→15^-}ax+b=15a+b=18$ ...(2)

eq. (2) - eq. (1)

$⇒10a=15$

$a=\frac{3}{2}$ from (1)

$5×\frac{3}{2}+b=3$

$b=\frac{-9}{2}$