Application of Derivatives Lecture 7

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अगर पाना है मंजिल तो, अपना रहनुमा खुद बनो,
वो अक्सर भटक जाते हैं, जिन्हें सहारा मिल जाता है।

Lecture - 7 Chapter 6 Application of Derivatives

In this lecture, I am discussing more questions based on tangents and normals from NCERT Exercise 6.3

Questions discussed in this lecture:

NCERT EXERCISE 6.3 (Tangents and Normals)

Question 15. Find the equation of the tangent line to the curve \( y = x^2 – 2x + 7 \) which is
(a) parallel to the line 2x – y + 9 = 0
(b) perpendicular to the line 5y – 15x = 13.

Question 16. Show that the tangents to the curve \( y = 7x^3 + 11\) at the points where x = 2 and x = – 2 are parallel.

Question 17. Find the points on the curve \( y = x^3\) at which the slope of the tangent is equal to the y-coordinate of the point.

Question 18. For the curve \( y = 4x^3 – 2x^5 \), find all the points at which the tangent passes through the origin.

Question 19. Find the points on the curve \( x^2 + y^2 -2x – 3 = 0 \) at which the tangents are parallel to the x-axis.

Question 20. Find the equation of the normal at the point \( (am^2, am^3) \) for the curve \( ay^2 = x^3 \).

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