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) \( f(x) = x \sqrt{1 – x}, 0<x<1 \)