# Lecture 11 Application of Derivatives P2

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 3x4 – 8x3 + 12x2 – 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 2x3 – 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 x4– 62x2 + 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].