Question:
Let $f(x) = \begin{cases}
|x|, & \quad \text{for}\, 0 < | x | \le 2 \\
1, & \quad \text{for} \, x = 0
\end{cases}$ then at x = 0, f has
Let $f(x) = \begin{cases}
|x|, & \quad \text{for}\, 0 < | x | \le 2 \\
1, & \quad \text{for} \, x = 0
\end{cases}$ then at x = 0, f has
Updated On: Jun 14, 2022
- a local maximum
- no local maximum
- a local minimum
- no extremum
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
It is clear from figure that at x = 0, f (x) is not differentiable .
$\Rightarrow$ f (x) has neither maximum nor minimum at x = 0
$\Rightarrow$ f (x) has neither maximum nor minimum at x = 0
Was this answer helpful?
0
0
Top Questions on Application of derivatives
- Evaluate the integral: \[ \int_{-\pi}^{\pi} x^2 \sin(x) \, dx \]
- VITEEE - 2024
- Mathematics
- Application of derivatives
- For the function $f(x) = x^3 - 6x^2 + 12x - 3$, $x = 2$ is:}
- KCET - 2024
- Mathematics
- Application of derivatives
- If \( \frac{dy}{dx} - y \log_e 2 = 2^{\sin x} (\cos x - 1) \log_e 2 \), then \( y \) is:
- BITSAT - 2024
- Mathematics
- Application of derivatives
- The solution of the differential equation \( (x + 1)\frac{dy}{dx} - y = e^{3x}(x + 1)^2 \) is:
- BITSAT - 2024
- Mathematics
- Application of derivatives
- If the area bounded by the curves \( y = ax^2 \) and \( x = ay^2 \) (where \( a>0 \)) is 3 sq. units, then the value of \( a \) is:
- BITSAT - 2024
- Mathematics
- Application of derivatives
View More Questions
Questions Asked in JEE Advanced exam
- Let \(S=\left\{\begin{pmatrix} 0 & 1 & c \\ 1 & a & d\\ 1 & b & e \end{pmatrix}:a,b,c,d,e\in\left\{0,1\right\}\ \text{and} |A|\in \left\{-1,1\right\}\right\}\), where |A| denotes the determinant of A. Then the number of elements in S is _______.
- JEE Advanced - 2024
- Matrices
- A positive, singly ionized atom of mass number \( A_M \) is accelerated from rest by the voltage \( 192 \, \text{V} \). Thereafter, it enters a rectangular region of width \( w \) with magnetic field \( \vec{B}_0 = 0.1\hat{k} \, \text{T} \). The ion finally hits a detector at the distance \( x \) below its starting trajectory. Which of the following option(s) is(are) correct? \[ \text{(Given: Mass of neutron/proton = } \frac{5}{3} \times 10^{-27} \, \text{kg, charge of the electron = } 1.6 \times 10^{-19} \, \text{C).} \]
- JEE Advanced - 2024
- Electromagnetic Field (EMF)
- A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass \( m \) and radius \( r \) and is in a uniform vertical magnetic field \( B_0 \). When a current \( I \) is passed through the loop, the loop turns about the line PQ by an angle \( \theta \). The angle \( \theta \) is given by:
- JEE Advanced - 2024
- Electromagnetic Field (EMF)
- A region in the form of an equilateral triangle (in x-y plane) of height \( L \) has a uniform magnetic field \( \mathbf{B} \) pointing in the \( +z \)-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height \( L \), is placed in the x-y plane with its vertex \( P \) at \( x = 0 \) in the orientation shown in the figure. At \( t = 0 \), the loop starts entering the region of the magnetic field with a uniform velocity \( \mathbf{v} \) along the \( +x \)-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graphs best depicts the variation of the induced emf (\( \mathcal{E} \)) in the loop as a function of the distance (\( x \)) starting from \( x = 0 \)?- JEE Advanced - 2024
- Radioactivity
- A table tennis ball has radius \( \frac{3}{2} \times 10^{-2} \, \text{m} \) and mass \( \frac{22}{7} \times 10^{-3} \, \text{kg} \). It is slowly pushed down into a swimming pool to a depth \( d = 0.7 \, \text{m} \) below the water surface and then released from rest. It emerges from the water surface at speed \( v \), without getting wet, and rises to a height \( H \). Which of the following option(s) is(are) correct?\(\text{(Given: } \pi = \frac{22}{7}, g = 10 \, \text{m/s}^2, \text{density of water} = 1 \times 10^3 \, \text{kg/m}^3, \text{viscosity of water} = 1 \times 10^{-3} \, \text{Pa.s).}\)
- JEE Advanced - 2024
- Radioactivity
View More Questions
Concepts Used:
Application of Derivatives
Various Applications of Derivatives-
Rate of Change of Quantities:
If some other quantity ‘y’ causes some change in a quantity of surely ‘x’, in view of the fact that an equation of the form y = f(x) gets consistently pleased, i.e, ‘y’ is a function of ‘x’ then the rate of change of ‘y’ related to ‘x’ is to be given by
\(\frac{\triangle y}{\triangle x}=\frac{y_2-y_1}{x_2-x_1}\)
This is also known to be as the Average Rate of Change.
Increasing and Decreasing Function:
Consider y = f(x) be a differentiable function (whose derivative exists at all points in the domain) in an interval x = (a,b).
- If for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≤ f(x2); then the function f(x) is known as increasing in this interval.
- Likewise, if for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≥ f(x2); then the function f(x) is known as decreasing in this interval.
- The functions are commonly known as strictly increasing or decreasing functions, given the inequalities are strict: f(x1) < f(x2) for strictly increasing and f(x1) > f(x2) for strictly decreasing.
Read More: Application of Derivatives