Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 2

f(x)=x^6-15x^5+75x^4-125x^3-x
f'(x)=6x^5-75x^4+300x^3-375x^2-1
f''(x)=30x^4-300x^3+900x^2-750x
See the attached graph and link. f is in red color , f' is in blue color and f'' is in green color.
From the graph ,
f is decreasing about on the intervals (-oo ,0) , (0,2.5) and (4.95,5.05)
f is increasing about on the intervals (2.5,4.95) and (5.05,oo )
Local maxima at x ~~ 4.95 ~~ 5
The function is concave up about on the intervals (-oo ,0) ,(1.4,3.6) and (5,oo )
function is concave down on the intervals (0,1.4) and (3.6,5)
Inflection points are (0,0) ,(5,-5) , (1.4,-130) and (3.6,-130)