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# How can write the following function ?

Posted 9 years ago
 {f[x] == (a x^3 + 6 x^2 + b)/(c x^2) with a?0 and b?0, Maximum relative (-2,0), oblique asymptotes ( y=2/3x + 2 )} Thanks Mike
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Posted 9 years ago
 I see. Continuing from above In:= y[x_] := (2 x^3 + 6 x^2 + b)/(3 x^2) In:= y'[-2] Out= (8 + b)/12 (* y'=0 gives b=-8 *) In:= Plot[(2 x^3 + 6 x^2 - 8)/(3 x^2), {x, -4, 4}] This gives your function
Posted 9 years ago
 In:= y[x_] := (a x^3 + 6 x^2 + b)/(c x^2) In:= y[x] Out= (b + 6 x^2 + a x^3)/(c x^2) In:= Expand[%] Out= 6/c + b/(c x^2) + (a x)/c As x->Infinity, asymptotic form implies c=3, a=2. Don't understand " Maximum relative (-2,0)"
Posted 9 years ago
 local maximum (relative maximum): a value of a function that is greater than those values of the function at the surrounding points, but is not the greatest of all values.
Posted 9 years ago
 In Mathematica execute Maximize[ {(a x^3 + 6 x^2 + b)/(c x^2), -2 < x < 0} , x] to get the full answer qualified by constraints on the parameters.
Posted 9 years ago
 How can qualified in Mathematica the constraints to get the full answer? Thanks a lot