Sketch the graph of a function f(x) that satisfies the stated conditions. Mark any inflection points by writing IP on your graph

50.a f is continuous and differentiable everywhere. b.f(0)=4 c. f'(x) < 0 on (-,-1) and (3,) d.f'(x) > 0 on (-1,3) e.f''(x) >0 on (-,1) f.f''(x) < 0 on (1, ) 51. a f is continuous and differentiable everywhere except at x=2, where it is undefined. b.f(0)=-1 c. Horizontal asymptote y=1 and vertical asymptote x=2 d. f'(x) < 0 wherever f' is defined 52.a f is continuous and differentiable everywhere except at x=-5 and x=5, where it is undefined b. f(0)=-1 c. Horizontal asymptote y=2 and vertical asymptotes x=-5 and x=5 d. f''(x) >0 on ( - ,-5) and ( 5,) e. f''(x) <0 on (-5,5) 53. a f is continuous everywhere and differentiable except at x =0 b.f(0)=3 c.f'(x)> 0 on (-,-2) and (0,2) d.f'(x) <0 on (-2,0) and (2, ) e.f''(x) <0 (-,0) (0,) 54. a f is continuous everywhere differentiable except at x =0 b. f(0) =5 c. f'(x) (-,-3) (0,3) d.> 0 on (-3,0) and (3, ) e. f''(x) > 0 on (-,0) and (0, )