Differentiating f(x) with respect to x, we get

Also, differentiating f’(x) with respect to x, we get

For maxima at x=c, f’(c)=0 and f’’(c)<0

⇒ or (Since x>0)

f’’(1)=2>0

Since f’’(1)>0 therefore x=1 is not a point of maxima and hence no maximum value of f(x) exists for x>0.