## Answers

11) tex) = 23-1270 2706+ 2 f'(21)=3*? 247-27 $"*7 = 63-24 We must have (@) For tex) to be iner increasing fraono 3 ² 24*-2770 x²8x-970 + + (2+1)(x-9) 70 7 1 9 x < -1 OR 279 il signs of f(x) for diffenent values of a. 2E (6-12 0(1) so, fca) is inerea increasing (-00,-1069,00) deenerring f'(xico For tex] to be dec We must have. > 3x² 242-27<o - (x+1)(x-9120 - 1 Lx29 OCE (-1,9) so, free) is deeneas decreasing on (-1,9)

Also, fx) Changes sign from negative to positive (b) We have, t'c20 = 3402 242-27 fixo = 3(x+2(3-9) x = o Now fragt - 3(x+12/X-92 = 0 넷 X = - 9 We have to examine whether these points are points of local manima ore local minina one neither of them. The changes in signs of f(x) for diffenent values of xe: are + + 7 1 2 an 1 . clearly fcxl changes sign from positive to negative x inereases through so, xant is a point of local manimum.

In the local manimum value of flag at x=-1 is f(-1) =(-123-126-12-27(-1)+2 - 16 x increases through a. so, x=9 is a point of local minimum. the local minimum value of fior) at a=q is 119) = 93- 12:19-27.(72+2 =[-484

We have, + 4 which f is concave (C) frase 620-24 ->)/(20) = 6(7-4) Now f"=0 -) 6(7-4)=0 x = 4 The changes in figns of t"cx for diffenert values of x are for fex ) to be con care up, we must have f'(xono - x-470 x>4 xe (4) 30, the required interval on when fis Contave up is [(4,0) Foro fix) to be coneare down, we must have f'(xico x24 = KE(-0,4) down is 1(x, 4) Now, af x=4 , 424) = 43–12:46–27.4 +2=-234 the required inflection point is (N,y) = (14.-234]). .

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