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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

POSTED BY: Mike Polik
5 Replies

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 BY: David Reiss
In[4]:= y[x_] := (a x^3 + 6 x^2 + b)/(c x^2)

In[5]:= y[x]

Out[5]= (b + 6 x^2 + a x^3)/(c x^2)

In[6]:= Expand[%]

Out[6]= 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 BY: S M Blinder
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 BY: Mike Polik
Posted 9 years ago

How can qualified in Mathematica the constraints to get the full answer? Thanks a lot

POSTED BY: Mike Polik

I see. Continuing from above

In[3]:= y[x_] := (2 x^3 + 6 x^2 + b)/(3 x^2)

In[4]:= y'[-2]

Out[4]= (8 + b)/12

(* y'[2]=0 gives b=-8 *)

In[5]:= Plot[(2 x^3 + 6 x^2 - 8)/(3 x^2), {x, -4, 4}]

This gives your function

POSTED BY: S M Blinder
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