jee-advanced 2005 Q16

jee-advanced · India · mains Stationary points and optimisation Determine parameters from given extremum conditions

16. If $p ( x )$ be a polynomial of degree 3 satisfying $p ( - 1 ) = 10 , p ( 1 ) = - 6$ and $p ( x )$ has maximum at $x = - 1$ and $p ^ { \prime } ( x )$ has minima at $x = 1$. Find the distance between the local maximum and local minimum of the curve.

A tangent at a point on the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ cuts the coordinate axes at $P$ and $Q$. The minimum area of the triangle $O P Q$ is

16. If $p ( x )$ be a polynomial of degree 3 satisfying $p ( - 1 ) = 10 , p ( 1 ) = - 6$ and $p ( x )$ has maximum at $x = - 1$ and $p ^ { \prime } ( x )$ has minima at $x = 1$. Find the distance between the local maximum and local minimum of the curve.\\

Paper Questions

Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18