Download App

6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The minimum value of the expression $7 - 20x + 11{x^2}$ is
  • A
    ${{177} \over {11}}$
  • B
    $ - {{177} \over {11}}$
  • ✓
    $ - {{23} \over {11}}$
  • D
    ${{23} \over {11}}$
✓

Answer

Correct option: C.
$ - {{23} \over {11}}$
c
(c) Given $f(x) = 7 - 20x + 11{x^2}$

$f'(x) = - 20 + 22x$

Put $f'(x) = 0$ $i.e.,$ $ - 20 + 22x = 0$

==> $x = 10/11$ and $f''(x) = 22 > 0$

Hence at $x = 10/11,\;\;\;f(x)$ will have minimum value,

$\therefore f\,\left( {\frac{{10}}{{11}}} \right) = 7 - \frac{{200}}{{11}} + \frac{{100 \times 11}}{{121}}$$ = 7 - \frac{{200}}{{11}} + \frac{{100}}{{11}}$

$ = - \frac{{23}}{{11}}$.

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 6. Application of derivatives→6. Application of derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is:
  1. Discontinuous at x = 0
  2. Continuous at x = 0
  3. Differentiable at x = 0
  4. None of these.
→
A value of $\theta  \in  (0, \pi /3)$, for which $\left| {\begin{array}{*{20}{c}}
  {1 + {{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\ 
  {{{\cos }^2}\,\theta }&{1 + {{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\ 
  {{{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{1 + 4\,\cos \,6\theta } 
\end{array}} \right| = 0$, is
→
The value of $\int_1^e \log x d x$ is
→
Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$ Then $f\left(\frac{7 \pi}{12}\right) f "\left(\frac{7 \pi}{12}\right)$ is equal to
→
Function $f(x) = {\sin ^{ - 1}}\left( {3x - 4{x^3}} \right)$ is
→
Let $x, y, z > 0$ are respectively $2^{nd}, 3^{rd}, 4^{th}$ term of $G.P.$ and $\Delta  = \left| {\begin{array}{*{20}{c}}
{{X^k}}&{{X^{k + 1}}}&{{X^{k + 2}}}\\
{{Y^k}}&{{Y^{k + 1}}}&{{Y^{k + 2}}}\\
{{Z^k}}&{{Z^{k + 1}}}&{{Z^{k + 2}}}
\end{array}} \right| = {\left( {r - 1} \right)^2}\left( {1 - \frac{1}{{{r^2}}}} \right)$ , (where $r$ is common ratio), then $k=$ .......
→
The points at which the function $f(x) = \frac{{x + 1}}{{{x^2} + x - 12}}$ is discontinuous, are
→
The range of the function $f(x) = \frac{x}{{1 + \left| x \right|}},\,x \in R,$ is
→
Let for $a \ne {a_1} \ne 0,$ $f\left( x \right) = a{x^2} + bx + c\;,g\left( x \right) = {a_1}{x^2} + {b_1}x + {c_1},p\left( x \right) = f\left( x \right) - g\left( x \right),$ If $p\left( x \right) = 0$ only for  $ x=-1 $ and $p\left( { - 2} \right) = 2$ then value of $p\left( 2 \right)$ is
→
The area under the curve  $y = \left| {\cos \,x - \sin \,x} \right|$ , $0 \leq x \leq\frac{\pi }{2}$, and above $x-$ axis is
→