jee-main 2019 Q82

jee-main · India · session2_09apr_shift1 Applied differentiation Tangent line computation and geometric consequences

Let $S$ be the set of all values of $x$ for which the tangent to the curve $y = f ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x$ at ( $x , y$ ) is parallel to the line segment joining the points $( 1 , f ( 1 ) )$ and $( - 1 , f ( - 1 ) )$, then $S$ is equal to
(1) $\left\{ - \frac { 1 } { 3 } , - 1 \right\}$
(2) $\left\{ - \frac { 1 } { 3 } , 1 \right\}$
(3) $\left\{ \frac { 1 } { 3 } , 1 \right\}$
(4) $\left\{ \frac { 1 } { 3 } , - 1 \right\}$

Let $S$ be the set of all values of $x$ for which the tangent to the curve $y = f ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x$ at ( $x , y$ ) is parallel to the line segment joining the points $( 1 , f ( 1 ) )$ and $( - 1 , f ( - 1 ) )$, then $S$ is equal to\\
(1) $\left\{ - \frac { 1 } { 3 } , - 1 \right\}$\\
(2) $\left\{ - \frac { 1 } { 3 } , 1 \right\}$\\
(3) $\left\{ \frac { 1 } { 3 } , 1 \right\}$\\
(4) $\left\{ \frac { 1 } { 3 } , - 1 \right\}$

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