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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

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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) \( f(x) = x \sqrt{1 – x}, 0<x<1 \)

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