`f(x) = x^6 - 15x^5 + 75x^4 - 125x^3 - x` Produce graphs of `f` that reveal all the important aspects of the curve. In particular, you should use graphs of `f'` and `f''`

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Chapter 4, 4.6 - Problem 2 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`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)

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