# Lecture 11 Application of Derivatives P4

A journey of a thousand miles begins with a single step. – Lao Tzu

# Part - 4 Lecture - 11 Chapter 6 Application of Derivatives

Topics discussed in this lecture:

Meaning of Local maxima, local minima, local maximum and local minimum
Second derivative test for local maxima and local minima

 NCERT EXERCISE 6.5

Questions discussed in this lecture

Question 3. Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:
(i) $$f(x) = x^2$$
(ii) $$g(x) = x^3 – 3x$$
(iii) $$h(x) = \sin x + \cos x , 0<x<\frac{\pi}{2}$$
(iv) $$f(x) = \sin x – \cos x , 0<x<2\pi$$
(v) $$f(x) = x^3 – 6x^2 + 9x + 15$$
(vi) $$g(x) = \frac{x}{2} + \frac{2}{x}, x>0$$
(vii) $$g(x) = \frac{1}{x^2 + 2}$$
(viii) $$f(x) = x \sqrt{1 – x}, 0<x<1$$