Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The minimum value of $(\text{x}^{2}+\frac{250}{\text{x}})$ is :
  • ✓
    $75$
  • B
    $50$
  • C
    $25$
  • D
    $55$
✓

Answer

Correct option: A.
$75$
$\text{f}(\text{x})=\text{x}^{2}+\frac{250}{\text{x}}$
$\text{f}\ '(\text{x})=2\text{x}-\frac{250}{\text{x}^{2}}$
For the local minima a or maxima.
We must have $f\ '(x) = 0$
$=2\text{x}-\frac{250}{\text{x}^{2}}=0$
$\Rightarrow x = 5$
$=2\text{x}-\frac{250}{\text{x}^{2}}=0$
$\text{f}\ ''(\text{x})=2+\frac{500}{\text{x}^{3}}$
$\text{f}\ ''(\text{x})=2+\frac{500}{125}>0$
function has minima at $x = 5$
$f(5) = 75.$

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 Application of Derivatives→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 number of real values of $x$ satisfying $\left| {\,\begin{array}{*{20}{c}} x&{3x + 2}&{2x - 1}\\{2x - 1}&{4x}&{3x + 1}\\{7x - 2}&{17x + 6}&{12x - 1}\end{array}\,} \right|$ $= 0$ is
→
The area of the region (in the square unit) bounded by the curve ${x^2} = 4y,$ line $x = 2$ and $x-$ axis is
→
Two matrices A and B are added if:
→
If $A=\left[\begin{array}{cc}\sin ^2 \theta & \sec ^2 \theta \\ \operatorname{cosec}^2 \theta & \frac{1}{2}\end{array}\right]$ and $B=\left[\begin{array}{cc}\cos ^2 \theta & -\tan ^2 \theta \\ -\cot ^2 \theta & \frac{1}{2}\end{array}\right]$ the value of $A + B$ will be :
→
If the system of equations, $x + 2y -3z = 1, (k + 3) z = 3, (2k + 1)x + z = 0$ is inconsistent, then the value of $k$ is :-
→
If $a = i + 2j - 3k$ and $b = 3i - j + 2k,$ then the angle between the vectors $a + b$ and $a - b$ is ............... $^o$
→
Let $f(x)=2+\cos x$ for all real $x$.

$STATEMENT -1$ : For each real $\mathrm{t}$, there exists a point $\mathrm{c}$ in $[\mathrm{t}, \mathrm{t}+\pi]$ such that $\mathrm{f}^{\prime}(\mathrm{c})=0$. because

$STATEMENT -2$: $f(t)=f(t+2 \pi)$ for each real $t$.

→
$\sin\big[\cot^{-1}\big\{\tan\big(\cos^{-1}\text{x}\big)\big\}\big]$ is equal to:
→
If $f$ is a real- valued differentiable function satisfying $|f(x) - f(y)| \le {(x - y)^2},x,y \in R$ and $f(0) = 0$, then $f(1)$ equal
→
If $\tan^{-1}(\text{x}-1)+\tan^{-1}\text{x}+\tan^{-1}(\text{x}+1)=\tan^{-1}3\text{x},$ then the values of $x$ are:
→