JEE Advanced · Mathematics · 23. C&D
If \(f(x)=\min \left\{1, x^2, x^3\right\}\), then
- A
\(f(x)\) is continuous everywhere
- B
\(f(x)\) is continuous and differentiable everywhere
- C
\(f(x)\) is not differentiable at two points
- D
\(f(x)\) is not differentiable at one point
Answer & Solution
Correct Answer
(D)
\(f(x)\) is not differentiable at one point
Step-by-step Solution
Detailed explanation
Here, \(f(x)=\min .\left\{1, x^2, x^3\right\}\) which could be graphically shown as
\[
\therefore \quad f(x)=\left\{\begin{array}{c}
1, x \geq 1 \\
x^3, x < 1
\end{array}\right.
\]
\[
\Rightarrow f(x) \text { is continuous for } x \in R \text { and not differentiable at } x=1 \text { due to sharp edge. }
\]
\[
\therefore \quad f(x)=\left\{\begin{array}{c}
1, x \geq 1 \\
x^3, x < 1
\end{array}\right.
\]
\[
\Rightarrow f(x) \text { is continuous for } x \in R \text { and not differentiable at } x=1 \text { due to sharp edge. }
\]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Mathematics
- Paragraph:
Let \(F_{1}\left(x_{1}, 0\right)\) and \(F_{2}\left(x_{2}, 0\right)\), for \(x_{1}<0\) and \(x_{2}>0\), be the foci of the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{8}=1 .\) Suppose a parabola having vertex at the origin and focus at \(F_{2}\) intersects the ellipse at point \(M\) in the first quadrant and at point \(N\) in the fourth quadrant.
Question:
If the tangents to the ellipse at \(M\) and \(N\) meet at \(R\) and the normal to the parabola at \(M\) meets the \(x\)-axis at \(Q\), then the ratio of area of the triangle \(M Q R\) to area of the quadrilateral \(M F_{1} N F_{2}\) isJEE Advanced 2016 Medium - In a non-right-angled triangle let denote the lengths of the sides opposite to the angles at respectively. The median from meets the side at the perpendicular from meets the side at , and and intersect at If and the radius of the circumcircle of the equals then which of the following options is/are correct?JEE Advanced 2019 Hard
- Let denote the complex conjugate of a complex number . If is a non-zero complex number for which both real and imaginary parts of are integers, then which of the following is/are possible value(s) of ?JEE Advanced 2022 Hard
- For let Then the possible value(s) of is/are:JEE Advanced 2019 Medium
- Let M be a symmetric matrix with integer entries. Then M is invertible ifJEE Advanced 2014 Easy
- The normal at a point \(P\) on the ellipse \(x^2+4 y^2=16\) meets the \(x\)-axis at \(Q\). If \(M\) is the mid-point of the line segment \(P Q\), then the locus of \(M\) intersects the latusrectum of the given ellipse at the pointsJEE Advanced 2009 Hard
More PYQs from JEE Advanced
- Let , be a continuous function then, which of the following function(s), has(have) the values zero at some point in the interval, (0,1)?JEE Advanced 2017 Hard
- A list of species having the formula XZ4 is given below.
\(\text{XeF} _4, \text{SF} _4, \text{SiF} _4, \text{BF} _4^{-}, \text{BrF} _4^{-},\left[\text{Cu} \left(\text{NH} _3\right)_4\right]^{2+},\) \(\left[\text{FeCl} _4\right]^{2-},\left[\text{CoCl} _4\right]^{2-}\) and \(\left[\text{PtCl} _4\right]^{2-}\)
Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape isJEE Advanced 2014 Easy - In thermodynamics, the work done is given by . For a system undergoing a particular process, the work done is,
. This equation is applicable to aJEE Advanced 2020 Hard - Let be a twice differentiable function such that for all . If , then which of the following statement(s) is (are) TRUE ?JEE Advanced 2018 Medium
- The colour of light absorbed by an aqueous solution of \(\mathrm{CuSO}_{4}\) is:JEE Advanced 2012 Medium
- A liquid at is poured very slowly into a Calorimeter that is at temperature of The boiling temperature of the liquid is It is found that the first of the liquid completely evaporates. After pouring another of the liquid the equilibrium temperature is found to be The ratio of the Latent heat of the liquid to its specific heat will be ______
[Neglect the heat exchange with surrounding]JEE Advanced 2019 Medium