Pretty much how to find the derivative of x(6-x)^(1/2)

[Silvet]

22. Consider a rectangle in the xy-plane with its lower-left vertex at the origin and its upper-right vertex on the graph of \(\displaystyle \, y\, =\, \sqrt{\vphantom{ [ }6\, -\, x\,}.\, \) What is the maximum area of such a rectangle? (image here:

< link to objectionable page removed >)

A. \(\displaystyle \sqrt{\vphantom{ [ }6\,}\). . .B. 4. . .C. \(\displaystyle 3\sqrt{\vphantom{ [ }3\,}\). . .D. \(\displaystyle 4\sqrt{\vphantom{ [ }2\,}\). . .E. \(\displaystyle 4\sqrt{\vphantom{ [ }6\,}\)

So I'm multiplying the contraint and the area formula, x(6-x)^(1/2), but finding the derivative is hard

Answer is D

 

[Deleted member 4993]

22. Consider a rectangle in the xy-plane with its lower-left vertex at the origin and its upper-right vertex on the graph of \(\displaystyle \, y\, =\, \sqrt{\vphantom{ [ }6\, -\, x\,}.\, \) What is the maximum area of such a rectangle? (image here: <link removed>)

A. \(\displaystyle \sqrt{\vphantom{ [ }6\,}\). . .B. 4. . .C. \(\displaystyle 3\sqrt{\vphantom{ [ }3\,}\). . .D. \(\displaystyle 4\sqrt{\vphantom{ [ }2\,}\). . .E. \(\displaystyle 4\sqrt{\vphantom{ [ }6\,}\)

So I'm multiplying the contraint and the area formula, x(6-x)^(1/2), but finding the derivative is hard

Answer is D

Use product rule and chain rule.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting