Let f(x) = * 20 c , x^3 - x^2 + 10x - 5 , ,, , , , , , , , , , , … - Vidyadip

MCQ

Let $f(x) = \left\{ {\begin{array}{*{20}{c}}
{\,{x^3} - {x^2} + 10x - 5\,\,,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\,\,\,\,\,}\\
{ - 2x + {{\log }_2}({b^2} - 2),\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, > 1\,\,\,\,\,\,\,\,\,\,\,\,}
\end{array}} \right.$ the set of values of $b$ for which $f(x)$ has greatest value at $x = 1$ is given by

A
$1 \le b \le 2$
B
$b = \{ 1,2\} $
C
$b \in ( - \infty , - 1)$
✓
$\left[ { - \sqrt {130} , - \sqrt 2 } \right) \cup \left( {\sqrt 2 ,\sqrt {130} } \right]$

✓

Answer

Correct option: D.

$\left[ { - \sqrt {130} , - \sqrt 2 } \right) \cup \left( {\sqrt 2 ,\sqrt {130} } \right]$

d
$f\left(1^{-}\right) \leq f(1)$ and $f\left(1^{+}\right) \leq f(1)$

$-2+\log _{2}\left(b^{2}-2\right) \leq 5$

$0 < {b^2} - 2 \le 128\quad 2 < {b^2} \le 130$

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 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\text{A} = \begin{bmatrix}1\end{bmatrix}$ then the order of the matrix is:

If a matrix $A$ is such that $3A^3 + 2A^2 + 5A + I = 0,$ then $A^{-1}$ equal to:

The value of objective function is maximum under linear constraints

If $A=\left|\begin{array}{lll}1 & -1 & 1 \\ 2 & -1 & 0 \\ 1 & 0 & 0\end{array}\right|$ then what is the value of $A^{-1}$.

If $x\,{\log _e}({\log _e}\,\,x)\, - \,{x^2} + {y^2} = 4\,(y\, > \,0),$ then $\frac{{dy}}{{dx}}$ at $x = e$ is equal to

Choose the correct answers from the given four options:
The derivative of $\cos^{-1}(2\text{x}^2-1)$ w.r.t. $\cos^{-1}\text{x}$ is:

The value of $\int_{}^{} {x\sin kx\;dx} $is

Define a function $f: R \rightarrow R$ by $f(x)=\left\{\begin{array}{cc}\frac{\sin x^2}{x}, & \text { for } x<0 \\ x^2+a x+b, & \text { for } x \geq 0\end{array}\right.$ Suppose $f(x)$ is differentiable of $R$. Then,

If three vectors $a, b, c$ satisfy $a + b + c = 0$ and $|a|\,\, = \,\,3,\,$ $|b|\, = 5,$ $|c|\,\, = 7,$ then the angle between $a$ and $b$ is .............. $^o$

If $y=y(x)$ is the solution of the equaiton $e ^{\sin y} \cos y \frac{ dy }{ dx }+ e ^{\sin y} \cos x =\cos x , y (0)=0$ then $1+ y \left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2} y \left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}} y \left(\frac{\pi}{4}\right)$ is equal to