Question:
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 < π/2 (iv) f(x) = sin x - cos x, 0 < x < 2π (v) f(x) = x^3 - 6x^2 + 9x + 15 (vi) g(x) = x/2 + 2/x, x > 0 (vii) g(x) = 1/(x^2 + 2) (viii) f(x) = x sqrt(1 - x), x > 0.