Exercise 5.2.10. Recall that a function f : (a, b) R is increasing on (a, b) if f (x) f (y) whenever x < y in (a, b). A familiar mantra from calculus is that a differentiable function is increasing if its derivative is positive, but this statement requires some sharpening in order to be completely accurate.Show that the functiong(x)= x/2+x2sin(1/x) ifx=00 if x =0is differentiable on R and satisfies g(0)>0. Now, prove that g is not increasing over any open interval containing 0.In the next section we will see that f is indeed increasing on (a, b) if and only if f(x)0 for all x in (a,b).