If f(x) = l a x^2 + b; , ,x 0 , , , , , , , , , x^2 ;x > 0 , . po… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}a{x^2} + b;\,\,x \le 0\\\,\,\,\,\,\,\,\,\,{x^2};x > 0\,\end{array} \right.$ possesses derivative at $x = 0$, then

A
$a = 0,b = 0$
B
$a > 0, = 0$
✓
$a \in R, = 0$
D
None of these

✓

Answer

Correct option: C.

$a \in R, = 0$

c
(c) $f(x)$ possesses derivative at $x = 0$, so it is both continuous and differentiable at $x = 0$.

Now $f(0 + 0) = 0$, $f(0 - 0) = b,f(0) = b$,

$\therefore \,\,b = 0$

Also $Rf'(0) = 0,Lf'(0) = 0,\forall a \in R$

$\therefore \,f'(0) = 0$ if $b = 0$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_{}^{} {\frac{{(x + 1){{(x + \log x)}^2}}}{x}dx = } $

If $y = a{e^{mx}} + b{e^{ - mx}}$, then ${{{d^2}y} \over {d{x^2}}} - {m^2}y = $

The direction cosines $l, m, n$ of two lines are connected by the relations $l + m + n = 0, lm = 0,$ then the angle between them is:

If A is a singular matrix, then adj A is.

If $\mid\text{a}\mid=5,\mid\text{b}\mid=13$ and $\mid\text{a}\times{\text{b}}\mid=25$ find $a.b:$

The differential equation of all straight lines passing through the origin is

Let $\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ be three unit vectors such that $|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{c}|^{2}=8$ Then $|\vec{a}+2 \vec{b}|^{2}+|\vec{a}+2 \vec{c}|^{2}$ is equal to

The solution of the differential equation $\frac{d y}{d x}+\frac{2 x y}{1+x^2}=\frac{1}{\left(1+x^2\right)^2}$ is:

The Image of the point (2, -1, 5) in the plane $\vec{\text{r}},\hat{\text{i}}=0$ is:

Using the factor theorem it is found that $a + b, b + c$ and $c + a$ are three factors of the determinant $\begin{vmatrix}-2\text{a}&\text{a}+\text{b}&\text{a}+\text{c}\\\text{b}+\text{a}&-2\text{b}&\text{b}+\text{c}\\\text{c}+\text{a}&\text{c}+\text{b}&-2\text{c}\end{vmatrix}$ the other factor in the value of the determinant is: