`y = x^3 - 6x^2 - 15x + 4` Sketch the curve by locating max/mins, asymptotes, points of inflection, etc.

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gsarora17 eNotes educator| Certified Educator


a) Asymptotes

Polynomial function of degree 1 or higher can't have any asymptotes.

b) Maxima/Minima




Now we can find critical numbers by solving x for y'=0,

`3(x-5)(x+1)=0rArrx=5 , x=-1`

Now let's check the sign of y' by plugging test points in the intervals (-`oo` ,-1) , (-1,5) and (5,`oo` )




Local Maximum at x=-1


Local Minimum at x=5


c) Inflection Points


Solve for x ,y''=0



Inflection point is (2,-42)

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