# `f(x) = 4x^4 - 32x^3 + 89x^2 - 95x + 29` 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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Expert Answers

gsarora17 | Certified Educator

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)

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