jee-main 2022 Q72

jee-main · India · session2_29jul_shift1 Stationary points and optimisation Find concavity, inflection points, or second derivative properties

Let $f ( x ) = 3 ^ { \left( x ^ { 2 } - 2 \right) ^ { 3 } + 4 } , \mathrm { x } \in R$. Then which of the following statements are true? $P : x = 0$ is a point of local minima of $f$ $Q : x = \sqrt { 2 }$ is a point of inflection of $f$ $R : f ^ { \prime }$ is increasing for $x > \sqrt { 2 }$
(1) Only $P$ and $Q$
(2) Only $P$ and $R$
(3) Only $Q$ and $R$
(4) All $P , Q$ and $R$

Let $f ( x ) = 3 ^ { \left( x ^ { 2 } - 2 \right) ^ { 3 } + 4 } , \mathrm { x } \in R$. Then which of the following statements are true?\\
$P : x = 0$ is a point of local minima of $f$\\
$Q : x = \sqrt { 2 }$ is a point of inflection of $f$\\
$R : f ^ { \prime }$ is increasing for $x > \sqrt { 2 }$\\
(1) Only $P$ and $Q$\\
(2) Only $P$ and $R$\\
(3) Only $Q$ and $R$\\
(4) All $P , Q$ and $R$

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