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A function f(x) having the followingproperties, (i) f(x) iscontinuous except at x=3 (ii) f(x) isdifferentiable except at x=-2 and x=3 (iii) f(0) =0 lim_( x to 3) f(x) to - oo lim_( x to -oo) f(x) =3 , lim_(x to oo ) f(x)=0 (iv) f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3) (v) f''(x) gt 0 AA x in (-oo,-2)uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo) Then answer the followingquestions Show that f'(x) +3x=0 has five solutions if f'(0) gt -3 " and " f(-2) gt6 |
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