Let $f(x)=\left\{\begin{array}{cc}a x, & x<2 \\ a x^2+b x+3, & x \geq 2\end{array}\right.$ If $f$ is differentiable for all $x$, then the value of ( $a$, b) is equal to

$\left(\frac{3}{2}, \frac{9}{2}\right)$

$\left(\frac{3}{4},-\frac{9}{2}\right)$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Hard

1 of 1

Application +4 | -1

Let

f(x)=\left\{\begin{array}{cc}a x, & x<2 \\ a x^2+b x+3, & x \geq 2\end{array}\right.

f

is differentiable for all

x

, then the value of (

a

, b) is equal to

View answer and explanation

Correct option: D

\left(\frac{3}{4},-\frac{9}{4}\right)

Option D (

\left(\frac{3}{4},-\frac{9}{4}\right)

) is correct because these values of a and b ensure that the function is both continuous and differentiable at x=2.