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) = x2 (ii) g(x) = x3 - 3 x (iii) h(x) = sin x + cos x, 0 2x π< < (iv) f (x) = sin x - cos x, 0 2 x< < π (v) f (x) = x3 - 6x2 + 9x + 15 (vi) 2( ) , 0 2 xg x x x= + > (vii) 2 / 1( ) / g x / x = + (viii) ( ) 1 , 0 1= − < <f x x x x