jee-advanced 2016 Q44

jee-advanced · India · paper2 Tangents, normals and gradients Find tangent line equation at a given point

Let $a , b \in \mathbb { R }$ and $f : \mathbb { R } \rightarrow \mathbb { R }$ be defined by $f ( x ) = a \cos \left( \left| x ^ { 3 } - x \right| \right) + b | x | \sin \left( \left| x ^ { 3 } + x \right| \right)$. Then $f$ is
(A) differentiable at $x = 0$ if $a = 0$ and $b = 1$
(B) differentiable at $x = 1$ if $a = 1$ and $b = 0$
(C) NOT differentiable at $x = 0$ if $a = 1$ and $b = 0$
(D) NOT differentiable at $x = 1$ if $a = 1$ and $b = 1$

Let $a , b \in \mathbb { R }$ and $f : \mathbb { R } \rightarrow \mathbb { R }$ be defined by $f ( x ) = a \cos \left( \left| x ^ { 3 } - x \right| \right) + b | x | \sin \left( \left| x ^ { 3 } + x \right| \right)$. Then $f$ is\\
(A) differentiable at $x = 0$ if $a = 0$ and $b = 1$\\
(B) differentiable at $x = 1$ if $a = 1$ and $b = 0$\\
(C) NOT differentiable at $x = 0$ if $a = 1$ and $b = 0$\\
(D) NOT differentiable at $x = 1$ if $a = 1$ and $b = 1$

Paper Questions

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