Monday

March 30, 2015

March 30, 2015

Posted by **Mark** on Tuesday, March 30, 2010 at 12:30am.

g(x) = 12 Ln x / x

My answer was: Domain = (12,0)

decreasing = (3,-2) and increasing = (-2,3) but these were wrong.

- Math(Please help) -
**Reiny**, Tuesday, March 30, 2010 at 8:29amFirst of all we can only take the ln of positive numbers,

so x > 0

(notice that also takes care of the possibility of dividing by zero)

g'(x) using the quotient rule was

(12 - 12lnx)/x^2

let's set that equal to zero for max/mins

12lnx = 12

lnx = 1

x = e

So when x = e the curve is neither increasing nor decreasing.

We could take the second derivative , but an easier way is to simply test a value less than and a value greater than e, and see if it is positive or negative.

We don't need that actual value

let x = 2

g'(2) = (12 - 12ln2)/4 , clearly positive , since ln2 is negative)

let x = 3

g'(3) = (12-l2ln3)/9 , which is negative

also if x = 3

g(e) = 12lne/e = 12/e = appr. 12/3 = appr.4

(calculator value =4.4145)

so...

domain : x > 0

increasing : 0 < x < e

decreasing: x > e

**Answer this Question**

**Related Questions**

Math - What is the domain? Use a graphing utility to determine the intervals in ...

Math(Help!!) - What is the domain? Use a graphing utility to determine the ...

Math - The directions say to use a grapking utility to approximate (to two-...

Math - Use a graphing utility to approximate (to two-decimal-place accuracy) any...

Pre-calculus - Use a graphing utility to approximate any relative minimum or ...

math - . Given the following function, f(x)=-x^2 -8x find: (a) vertex, (b) axis...

pre-cal: graphs of functions- fill in the blank - To find the domain of a ...

Pre-Calculus - 1) Use a graphing utility to obtain the graph of the function. ...

algebra - Given the following function, find: (a) vertex (b) axis of symmetry (c...

precalculus - Use the Intermediate Value Theorem and a graphing utility to find...