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.
$
Answer & explanation
Correct answer: option 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)
$5×\frac{3}{2}+b=3$
$b=\frac{-9}{2}$