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.