Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 1

See the attached graphs and links. f(x) is in red color , f'(x) in blue color and f''(x) in green color.Graphs are plotted in various ranges to have clarity.
From the graphs f(x)=0 hArr x=0.5 , 1.60
f'x)=0 hArr x ~~ 0.925 , 2.5 , 2.575
f''(x)=0 <=> x~~ 1.45 , 2.55
From the graph of f'(x)
f'(x)< 0 , f is decreasing on (-oo , 0.925) and (2.5,2.575)
f'(x)> 0 , f is increasing on (0.925,2.5) and (2.575,oo )
Local minimum value f(0.925)~~ -5.125, f(2.575) ~~ 3.995
Local maximum value f(2.5) ~~ 4
From the graph of f''(x) ,
f''(x)> 0 , f is Concave up on (-oo ,1.45) and(2.55,oo )
f''(x)< 0 , f is Concave down on (1.45,2.55)
Inflection points at about (1.45,-1.50) and (2.55 , 4.0)