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NCERT Class 12- Mathematics: Chapter β 6 Application of Derivatives Part 3
Question 8:
Find the condition for the curves o intersect orthogonally.
Answer:
Let the curves intersect at . Therefore,
Slope of tangent at the point of intersection
Again
For orthoganality,
Question 9:
Find all the points of local maxima and local minima of the function
Answer:
. Therefore, is point of local maxima
. Therefore, is point of local minima
. Therefore is point of local maxima.
Question 10:
Show that the local maximum value of is less than local minimum value.
Answer:
Let
Hence local maximum value of is at and the local maximum value .
Local minimum value of is at and local minimum value .
Therefore, local maximum value is less than local minimum value .
Long Answer Type (L. A.)
Question 11:
Water is dripping out at a steady rate of rough a tiny hole at the vertex of the conical vessel, whose axis is vertical. When the slant height of water in the vessel is , find the rate of decrease of slant height, where the vertical angle of the conical vessel is
Answer:
Given that , where v is the volume of water in the conical vessel.
From the Fig 6.2,
Therefore,
Therefore,
Therefore, the rate of decrease of slant height
Question 12:
Find the equation of all the tangents to the curve , that are parallel to the line .
Answer:
Given that
Or
Since tangent is parallel to , therefore slope of tangent
Therefore,
Since .
Therefore,
Therefore,
Thus, satisfy equation (ii)
Hence, the points are
Therefore, equation of tangent at and equation of tangent at