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) = x²

(ii) g(x) = x³ – 3x

(iii) h(x) = sinx + cosx, o < x< \(\frac{\pi}{2}\)

(iv) f(x) = sinx – cosx, 0 < x < 2π

Answer 1

(i) f(x) = x²

f’(x) = 2x, f’(x) = 0

⇒ 2x = 0, x = 0

f'(x)= 2

f'(x)> 0, hence f (x) has minimum value at x = 0

and the minimum value is (0)²= 0

(ii) 

(iii)

(iv)