Algebra help

[Sarawr]

Hi, I'm having trouble with this question.

Find the minimum for y
y=(a+x)(b+x)\cx
c,x,b,a>0

Can anyone help? Thanks.

 

[mmm4444bot]

… y=(a+x)(b+x)\cx …

Is what you typed supposed to be a rational function?

y = [(x + a)(x + b)]/(cx)

Does this exercise come from a calculus course? Are you trying to use the derivative? Why are you stuck?

The more information that you provide to tutors, the better the responses that you will get back. Otherwise, we'll be playing a guessing game.

Tell us what you already know about this exercise, and please check out the 'Read Before Posting' message.

 

[Denis]

Find the minimum for y
y=(a+x)(b+x)\cx
c,x,b,a>0

Hmmm....kinda silly....since c is in denominator, then minimum y = maximum c !

 

[mmm4444bot]

With a, b, and c representing arbitrary and fixed positive Real constants, the Quadrant I minimum of the rational function y = (x + a)(x + b)/(cx) is:

\(\displaystyle y \,=\, \frac{a}{c} \,+\, \frac{b}{c} \,+\, \frac{2ab}{c \; \sqrt{ab}}\)

Unless I goofed.