what is the minimum value of the product P=xy when y=5+3x

Question

mathmale · Answer

Write out the product as given:  xy

Replace the y in xy with y as a function of x (which is explicitly given).  Doing this eliminates y from consideration for the time being.

Multiply out the product x( ?? ).

Differentiate the result.  Set your derivative = to 0.  Solve for the critical values.  

If you're not yet in calculus, then instead of "Differentiate the result," arrange the terms of the result in descending order by powers of x.

Set this expression = to 0.  Solve for x (e. g., thru using the quadratic formula).  Your two results are the x-intercepts.

Find the value of x at which your expression xy is at its one and only maximum.

mathmale · Answer

Apologies.  Where I've written "maximum," I should have written "minimum."  But you can easily fix that by substituting "max" for "min."

thatonegirl_ · Answer

ah thank you so much!!! :D