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# Lecture - 5 Chapter 6 Application of Derivatives

In this lecture, I am discussing basics of slope of tangent, slope of normal, slope of parallel lines, slope of perpendicular lines, equation of tangent, equation of normal and questions based on these topics from NCERT Exercise 6.3

**Questions discussed in this lecture:**

NCERT EXERCISE 6.3 (Tangents and Normals) |

**Question 1.** Find the slope of the tangent to the curve \( y = 3x^4 – 4x \) at x = 4.

**Question 2.** Find the slope of the tangent to the curve \( y = \frac{x – 1}{x – 2}, x \ne 2 \) at x =10.

**Question 3.** Find the slope of the tangent to curve \( y = x^3 – x + 1 \) at the point whose x-coordinate is 2.

**Question 4.** Find the slope of the tangent to curve \( y = x^3 – 3x + 2 \) at the point whose x-coordinate is 3.

**Question 5.** Find the slope of the normal to the curve \( x = a \cos^3 \theta, y = a \sin^3 \theta \) at \( \theta = \frac{\pi}{4}\).

**Question 6.** Find the slope of the normal to the curve \( x = 1 – a \sin \theta, y = b \cos^2 \theta \) at \( \theta = \frac{\pi}{2}\).

**Question 7.** Find points at which the tangent to the curve \( y = x^3 – 3x^2 – 9x + 7 \) is parallel to the x – axis.

**Question 8.** Find a point on the curve \( y = (x – 2)^2 \) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).