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

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

(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) $$f(x) = x \sqrt{1 – x}, 0<x<1$$