`f(x) = x^6 - 10x^5 - 400x^4 + 2500x^3` Produce graphs of `f` that reveal all the important aspects of the curve. In particular, you should use graphs of `f'` and `f''`

Expert Answers
gsarora17 eNotes educator| Certified Educator

See the attached graph of f(image) in red color and links.Graph is drawn on two ranges for better clarity.

From the graph , f is decreasing on intervals (-`oo` ,-15) and (4.40,19.0)

f is increasing on intervals (-15,4.40) and (19,`oo` )

Local minimum f(-15) `~~` -9,687,500 f(19) `~~` -12,500,000

Local maximum f(4.4) `~~` 54,000

See the graph of f' in link blue color

graph of f'' in link green color

From the graph

Function is concave up on the intervals (-`oo` ,-11) , (0,3) and (15,`oo` )

Function is concave down on the intervals (-11,0) and (3,15)

Inflection points at x=0 , x `~~` -11 , 3 , -15` `

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