Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2. Then, f(x) has a minimum at x= - Vidyadip

MCQ

Let $f(x)=(x-a)^2+(x-b)^2+(x-c)^2.$ Then, $f(x)$ has a minimum at $x=$

✓
$\frac{\text{a}+\text{b}+\text{c}}{3}$
B
$\sqrt[3]{\text{a}\text{b}\text{c}}$
C
$\frac{3}{\frac{1}{\text{a}}+\frac{1}{\text{b}}+\frac{1}{\text{c}}}$
D
None of these.

✓

Answer

Correct option: A.

$\frac{\text{a}+\text{b}+\text{c}}{3}$

$f(x)=(x-a)^2+(x-b)^2+(x-c)^2$
$\Rightarrow 2(x-a)+2(x-b)+2(x-c)$
to find minima or maxima $f ^{\prime}(x)=0$
$2(x-a)+2(x-b)^2+2(x-c)=0$
$\Rightarrow x=\frac{a+b+c}{3}$
$f^{\prime \prime}(x)=6>0$
function has minima at $\text{x}=\frac{\text{a}+\text{b}+\text{c}}{3}$.

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

If $a, b, c $ are position vector of vertices of a triangle $ABC$, then unit vector perpendicular to its plane is

If $f(x) = \left\{ \begin{array}{l}\frac{{1 - \cos x}}{x},\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k,\,x = 0\end{array} \right.$ is continuous at $x = 0$ then $k = $

Let $z=\frac{-1+\sqrt{3} i}{2}$, where $i=\sqrt{-1}$, and $r, s \in\{1,2,3\}$. Let$P=\left[\begin{array}{cc}(-z)^r & z^{2 s} \\ z^{2 s} & z^r\end{array}\right]$ and $I$ be the identity matrix of order $2$ . Then the total number of ordered pairs $(r, s)$ for which $P^2=-I$ is

$\text{f}(\text{x})=\sin +\sqrt{3}\cos\text{x}$ is maximum when $x =$

The coordinates of the point on the ellipse $16 x^2+9 y^2=400$ where the ordinate decreases at the same rate at which the abscissa increases, are :

$\int_{}^{} {\frac{{x\;dx}}{{1 - x\cot x}}} = $

Let $f(x)$ and $g(x)$ be differentiable functions on $R$ . If $h(x) = f(g(f(x)))$ , where $f(2) = 1$ , $g(1) = 2$ and $f'(2) = g'(1) = 4$ , then $h'(2)$ is equal to

For the matrix $A = \left[ {\begin{array}{*{20}{c}}1&1&0\\1&2&1\\2&1&0\end{array}} \right]$, which of the following is correct

Let $f, g: R \to R$ be two functions defined by $f(x)\, = \,\left\{ {\begin{array}{*{20}{c}}
{x\,\sin \,\left( {\frac{1}{x}} \right),\,x\, \ne \,0\,\,\,\,\,\,\,\,\,\,}\\
{0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x\, = 0\,\,\,\,\,\,\,\,\,}
\end{array}} \right.,$ and $g(x) =x\,f(x)$

Statement $I:$ $f$ is a continuous function at $x = 0.$
Statement $II:$ $g$ is a differentiable function at $x = 0.$

A box contains $b$ blue balls and $r$ red balls. A ball is drawn randomly from the box and is returned to the box with another ball of the same colour. The probability that the second ball drawn from the box is blue, is