A real valued function y = f(x) satisfies the relation f ( x - 4 … - Vidyadip

MCQ

A real valued function $y = f(x)$ satisfies the relation $f\left( {x - \frac{4}{9}} \right) + 2x \le \frac{9}{4}{x^2} + \frac{8}{9} \le f\left( {x + \frac{4}{9}} \right) - 2x$ . The value of $f\ ''(2)$ is

A
$4$
✓
$\frac {9}{2}$
C
$\frac {15}{2}$
D
$\frac {27}{2}$

✓

Answer

Correct option: B.

$\frac {9}{2}$

b
$f(x)=\frac{9}{4} x^{2}+\frac{4}{9}$

$f^{\prime}(x)=\frac{9}{2} x$

$f^{\prime}(x)=\frac{9}{2}$

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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\Delta = \left| {\,\begin{array}{*{20}{c}}a&b&c\\x&y&z\\p&q&r\end{array}\,} \right|$, then $\left| {\,\begin{array}{*{20}{c}}{ka}&{kb}&{kc}\\{kx}&{ky}&{kz}\\{kp}&{kq}&{kr}\end{array}\,} \right|$=

The maximum value of Z = 3x + 4y subjected to contraints $\text{x}+\text{y}\leq40,\text{x}+2\text{y}\leq60,\text{x}\geq0$ and $\text{y}\geq0$ is:

120
140
100
160

$\int\limits_{ - \,1}^1 {\,\,\frac{{{x^3}\, + \,\,|x|\,\, + \,\,1}}{{{x^2}\, + \,\,2\,|x|\,\, + \,\,1}}}\,dx$ $= a\, ln\, 2 + b$ then :

If $\vec{\text{a}}.\hat{\text{i}}=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}\big)=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)=1.$then $\vec{\text{a}}=$

$\vec{0}$
$\hat{\text{i}}$
$\hat{\text{j}}$
$\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$

The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is:

An ellipse
Parabola
Circle
Hyperbola

Let $g(x)=\log (f(x))$ where $f(x)$ is a twice differentiable positive function on $(0, \infty)$ such that $f(x+1)=x f(x)$. Then, for $\mathrm{N}=1,2,3, \ldots$,

$\mathrm{g}^{\prime \prime}\left(\mathrm{N}+\frac{1}{2}\right)-\mathrm{g}^{\prime \prime}\left(\frac{1}{2}\right)=$

A set of vectors taken in a given order gives a closed polygon.Then the resultant of these vectors is:

scalar quantity
pseudo vector
unit vector
null vector

If the projection of $\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ on $\vec{\text{b}}=2\hat{\text{i}}+\lambda\hat{\text{k}}$ is zero, then the value of $\lambda$ is:

$0$
$1$
$\frac{-2}{3}$
$\frac{-3}{2}$

Consider a differential equation of order mm and degree nn. Which one of the following pairs is not feasible?

$(3,2)$
$(2,\frac{3}{2})$
$(2,4)$
$(2,2)$

Let ${\tan ^{ - 1}}\left( {\tan \frac{{5\pi }}{4}} \right) = \alpha ,{\tan ^{ - 1}}\left( { - \tan \frac{{2\pi }}{3}} \right) = \beta $ Then :-