NCERT Class 12-Mathematics: Chapter – 6 Application of Derivatives Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)
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Question 13:
Find the angle of intersection of the curves and .
Answer:
Given that and (ii) . Solving (i) and (ii) , we get
Or
Therefore, the points of intersection are and
Again,
Therefore, at the tangent to the curve is parallel to axis and tangent to the curve is parallel to axis.
Angle between curves
Therefore,
Hence,
Question 14:
Show that the equation of normal at any point on the curve nswer:
We have
Therefore,
Therefore, slope of normal
Hence the equation of normal is
Or
Question 15:
Find the maximum and minimum values of
Answer:
Therefore,
Therefore, possible values of are , or and
Again,
. We note that
. Therefore, is a point of maxima.
. Therefore, is a point of maxima.
. Therefore, is a point of minima.
. Therefore, is a point of minima.