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 function $y = 2{x^3} - 21{x^2} + 36x - 20$ is
  • ✓
    $-128$
  • B
    $-126$
  • C
    $-120$
  • D
    None of these
✓

Answer

Correct option: A.
$-128$
a
(a) Given, $f(x) = 2{x^3} - 21{x^2} + 36x - 20$

$f'(x) = 6{x^2} - 42x + 36$

Put $f'(x) = 0$==> $6{x^2} - 42x + 36 = 0$==> ${x^2} - 7x + 6 = 0$

==> ${x^2} - 6x - x + 6 = 0$==> $(x - 1)(x - 6) = 0$==> $x = 1,\,6$

Now, $f''\,(x) = 12x - 42$

$f''\,(1) = - 30 = - ve$ and $f''\,(6) = 30 = + ve$

Hence $x = 6$ is the point of minima

$\therefore$ Minimum value = $f(6) = 2{(6)^3} - 21{(6)^2} + 36 \times 6 - 20$

$\therefore$ $f(6) = - 128$.

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

Find the cofactor of element -3 in the determinant $\triangle=\begin{bmatrix}1&4&4\\-3&5&9\\2&1&2\end{bmatrix}$ is:
  1. -4
  2. 4
  3. -5
  4. -3
→
Let three matrices $A =$$\left[ {\begin{array}{*{20}{c}}2&1\\4&1\end{array}} \right]$ ; $B =$$\left[ {\begin{array}{*{20}{c}}3&4\\2&3\end{array}} \right]$ and $C =$$\left[ {\begin{array}{*{20}{c}}3&{ - 4}\\{ - 2}&3\end{array}} \right]$ then $T_r(A) + t_r$ $\left( {\frac{{ABC}}{2}} \right)$ $+$ $t_r$$\left( {\frac{{A{{(BC)}^2}}}{4}} \right)$  $+$ $t_r$ $\left( {\frac{{A{{(BC)}^3}}}{8}} \right)$ $+$ ....... $+ \infty =$
→
If $\int \frac{\mathrm{d} \theta}{\cos ^{2} \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _{\mathrm{e}}|\mathrm{f}(\theta)|+\mathrm{C}$  where $\mathrm{C}$ is a constant of integration, then the ordered pair $(\lambda, f(\theta))$ is equal to
→
$\int_0^{\pi /3} {\cos 3x\,dx = } $
→
Let $A = \,\left[ {\begin{array}{*{20}{c}}
1&0&0\\
1&1&0\\
1&1&1
\end{array}} \right]$ and $B = A^{20}$ . Then the sum of the elements of the first column of $B$ is?
→
The area of the region bounded by the $x - $ axis and the curves defined by $y = \tan x,\,( - \pi /3 \le x \le \pi /3)$ is
→
In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math?
→
Let A = {1, 2, 3}. Then the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive is:
  1. 1
  2. 2
  3. 3
  4. 4
→
If $f: R \rightarrow R, f(x)=2 x+1$, then the value of $f^{-1}(5)$ is
→
Let $f(x)$ be a differentiable function which satisfies the equation $f(xy) = f(x) + f(y)$ for all $x > 0, y > 0$ then $f ‘(x)$ is equal to
→