3. Recall that if a differentiable function f is increasing on an open interval I, then f'(x) 20 for all x E I, and if f is decreasing on I, then f'(x) 50 for xE I. [10] Exercise (a) shows that even if a differentiable function f has f'(c) >0, it may not be true that f is increasing near c (precisely, in an open interval containing c). Exercise (b) shows that even if a differentiable function f has a local minimum value at c, it may not be true that f is decreasing on the left of c and increasing on the right of c. (a) Let f (x) = x+3x sin(1/x) ifx#0, if x = 0. MA2002 CALCULUS HOMEWORK ASSIGNMENT 3 2 (i) Find the value of f' (0). (ii) For any o > 0, find a number ce (-6,6) such that f'(c) 0, find a number ci E (-6,0) such that f'(c1) > 0 and a number C2 E (0,6) such that f'(c2)