Proof: Let . EIX] be arbitrary. Using openness of IJ, choose 8>0 such that 1-8, +8xx-8x+8 0 with the property. K for all E-8, +8 and for all xx-8.x +8. Ox Finally let 1-8, +6 x, y in x-8, x+8 be arbitrary. By the mean value theorem of differential calculus, we have: Of ft.y-f(t,x)=(y-x)1,Z Ox for some z between x and y. Therefore, - (Since 1,2 1-8, +8xx 8x+8 and therefore 0. Proof Choose >0 such that 1-8, +8 0, M> 0, chosen above, we choose one more constant satisfying 0