Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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

Determine the value of $k$ for which the function $f(x)$ is continuous at $x=4$.
$
f(x)=\left\{\begin{array}{ll}
\frac{x^2-16}{x-4}, & x \neq 4 \\
k, & x=4
\end{array}\right.
$
→
Adjoint of the matrix $N = \left[ {\begin{array}{*{20}{c}}{ - 4}&{ - 3}&{ - 3}\\1&0&1\\4&4&3\end{array}} \right]$is
→
$\left| {\,\begin{array}{*{20}{c}}1&{1 + ac}&{1 + bc}\\1&{1 + ad}&{1 + bd}\\1&{1 + ae}&{1 + be}\end{array}\,} \right| = $
→
Let $u = i + j, v = i -j$ and $w = i + 2j + 3k$. If $n$ is a unit vector such that $u.n = 0$ and $v.n = 0$ then $|w\,.\,n|$ is equal to
→
The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8\hat i - 6\hat j$ and $3\hat i + 4\hat j - 12\hat k$ , is
→
The cubic $\left| {\begin{array}{*{20}{c}}
  0&{a - x}&{b - x} \\ 
  { - a - x}&0&{c - x} \\ 
  { - b - x}&{ - c - x}&0 
\end{array}} \right| = 0$ has a reperated root in $x$ then,
→
Evaluate: $\int_0^{\pi / 4} \tan ^3 x d x$
→
For the differential equation $x \frac{d y}{d x}+2 y=x y \frac{d y}{d x}$, which of the following is true?
→
The number of points in $\left( { - \infty ,\infty } \right)$, for which $x^2 -x\, sin\,x -cos\,x = 0$, is
→
$\int\log_{10}\text{xdx}=$
  1. $\log_{\text{e}}10.\text{x}\log_{\text{e}}\big(\frac{\text{x}}{\text{e}}\big)+\text{c}$
  2. $\log_{10}\text{e.x}\log_{\text{e}}\big(\frac{\text{x}}{\text{e}}\big)+\text{c}$
  3. $\log_{10}\text{e.x}\log_{\text{e}}\big(\frac{\text{x}}{\text{e}}\big)+\text{n}$
  4. $\log_{10}\text{e.x}\log_{\text{e}}\big(\frac{\text{x}}{\text{n}}\big)+\text{n}$
→