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JEE Advanced 2006

Exam: JEE Advanced
Year: 2006
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Advanced 2006 · Mathematics · Continuity and Differentiability

If f(x)= \ 1, x^2, x^3\ , then

If

f(x)=\min \left\{1, x^2, x^3\right\}

, then $If f(x)= \ 1, x^2, x^3\ , then$ $If f(x)= \ 1, x^2, x^3\ , then$

Options

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

Correct answer

A. $f(x)$ is continuous everywhere

Step-by-step solution

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 \\ x³, x < 1 \end{array}

\right.

$If f(x)= \ 1, x^2, x^3\ , then$

\\ \Rightarrow f(x) \text{ is continuous for }x \in R \text{ and not differentiable at }x=1 \text{ due to sharp edge. }

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