Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,904 users

I am trying to find the critical values of ln((x^2+4)^(1/2)

0 votes

I found they are 0,2, and -2. I just wanted some conformation.?  

asked Nov 13, 2014 in PRECALCULUS by anonymous

1 Answer

0 votes

The function f(x) = ln(√(x2 + 4)

Apply derivative with respect to x.

d/dx[f(x)] = d/dx[ln(√(x2 + 4)]

Recall the formulae: d/dx[ln(x)] = 1/x

d/dx[√x] = 1/(2√x)

d/dx[xn] = 1/xn-1

d/dx[constant] = 0

f'(x) = [1/√(x2 + 4)] [1/2(√(x2 + 4))] [2x]

f'(x) = 2x/[2(x2 + 4)]

f'(x) = x/(x2 + 4)

f'(x) is undefined at x = 2 and - 2 is included in the domain of f .

To find critical values equate the first derivative to 0.

x/(x2 + 4) = 0

x = 0

Critical points are at x = 0, 2 and - 2.

answered Nov 13, 2014 by david Expert

Related questions

asked Oct 25, 2014 in PRECALCULUS by anonymous
asked Jul 22, 2014 in CALCULUS by anonymous
asked Oct 11, 2014 in PRECALCULUS by anonymous
...