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If $f(x)=\min \left\{1, x^2, x^3\right\}$, then
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2560 Upvotes
Verified Answer
The correct answers are:
$f(x)$ is continuous everywhere
,
$f(x)$ is not differentiable at one point
$f(x)$ is continuous everywhere
,
$f(x)$ is not differentiable at one point
Here, $f(x)=\min .\left\{1, x^2, x^3\right\}$ which could be graphically shown as
$$
\therefore \quad f(x)=\left\{\begin{array}{c}
1, x \geq 1 \\
x^3, x < 1
\end{array}\right.
$$
$$
\Rightarrow f(x) \text { is continuous for } x \in R \text { and not differentiable at } x=1 \text { due to sharp edge. }
$$
$$
\therefore \quad f(x)=\left\{\begin{array}{c}
1, x \geq 1 \\
x^3, x < 1
\end{array}\right.
$$
$$
\Rightarrow f(x) \text { is continuous for } x \in R \text { and not differentiable at } x=1 \text { due to sharp edge. }
$$
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