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# Lecture - 10 Chapter 6 Application of Derivatives

In this lecture, I am discussing method to find approximate values of roots using derivatives and questions from NCERT Exercise 6.4

**Questions discussed in this lecture:**

NCERT EXERCISE 6.4 (Approximations) |

**Question 2.** Find the approximate value of f(2.01), where \( f(x) = 4x^2 + 5x +2\).

**Question 3.** Find the approximate value of f(5.001), where \( f(x) = x^3 – 7x^2 +15\).

**Question 4.** Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

**Question 5.** Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

**Question 6.** If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

**Question 7.** If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.

**Question 8.** If \( f(x) = 3x^2 + 15x + 5 \), then the approximate value of f (3.02) is

(A) 47.66

(B) 57.66

(C) 67.66

(D) 77.66

**Question 9.** The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

(A) \( 0.06 x^3 m^3 \)

(B) \( 0.6 x^3 m^3 \)

(C) \( 0.09 x^3 m^3 \)

(D) \( 0.9 x^3 m^3 \)