The successful warrior is the average man, with laser-like focus. – **Bruce Lee**

# Part - 2 Lecture - 11 Chapter 6 Application of Derivatives

**Topics discussed in this lecture:**

Meaning of Absolute Maximum and Absolute Minimum. Method to find Absolute Maxima and Absolute Minima

NCERT EXERCISE 6.5 |

**Questions discussed in this lecture**

**Question 5. **Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:

(i) \( f(x) = x^3, x \in [-2, 2] \)

(ii) \( f(x) = \sin x + \cos x, x \in [0, \pi] \)

(iii) \( f(x) = 4x – \frac{1}{2}x^2, x \in \left[-2, \frac{9}{2} \right] \)

(iv) \( f(x) = (x – 1)^2 + 3, x \in [-3, 1] \)

**Question 7. **Find both the maximum value and the minimum value of 3x^{4 }– 8x^{3} + 12x^{2} – 48x + 25 on the interval [0, 3].

**Question 8. **At what points in the interval [0, 2π], does the function sin 2x attain its maximum value?

**Question 9. **What is the maximum value of the function sin x + cos x?

**Question 10. **Find the maximum value of 2x^{3} – 24x + 107 in the interval [1, 3]. Find the

maximum value of the same function in [–3, –1].

**Question 11.** It is given that at x = 1, the function x^{4}– 62x^{2 }+ ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.

**Question 12.** Find the maximum and minimum values of x + sin 2x on [0, 2π].