MCQ
For which value of $x$ , the function $f(x) = {x^2} - 2x$ is decreasing
- A$x > 1$
- B$x > 2$
- ✓$x < 1$
- D$x < 2$
✓
Answer
Correct option: C.
$x < 1$
c
(c) $f(x) = {(x - 1)^2} - 1$. Hence decreasing in $ x < 1.$
(c) $f(x) = {(x - 1)^2} - 1$. Hence decreasing in $ x < 1.$
Aliter : $f'(x) = 2x - 2 = 2(x - 1)$
To be decreasing, $2(x - 1) < 0 \Rightarrow (x - 1) < 0 \Rightarrow x < 1$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=1,|\vec{b}|=2$ and $\vec{a} \cdot \vec{b}=\sqrt{3}$, then the angle between $2 \vec{a}$ and $-\vec{b}$ is:
→If $\vec a$ and $\vec b$ are non-zero vectors which are linearly dependent such that $\frac{{\left| {\vec a + \vec b} \right|}}{{\left| {\vec a - \vec b} \right|}}\, = \,2,\,\left| {\vec b} \right|\, > \,\left| {\vec a} \right|$ Then
→If integrating factor of $x(1 - {x^2})dy + (2{x^2}y - y - a{x^3})dx = 0$ is ${e^{\int_{}^{} {Pdx} }},$ then $P$ is equal to
→The value of $y ($breadth of rectangular field$)$ is:
→Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A ^{2}$ is $1,$ then the possible number of such matrices is
→Let $f (x + y) = f (x) + f (y)$ for all $x , y \in R.$ Then :
→If $A$ and $B$ are square matrices of same order and $|B| \neq 0$ then $(B^{-1}\,AB)^5$ is equal to
→The cartesian equation of the line which passes through the point $(-2,4,-5)$ and parallel to the line given by $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is
→If $\cos\alpha,\cos\beta,\cos\gamma$ are the direction cosines of a vector $\vec{\text{a}}$ then $\cos2\alpha+\cos2\beta+\cos2\gamma$ is equal to:
→$\int_0^\pi {{{\sin }^2}x\,dx} $ is equal to
→