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.

13,338 questions

17,804 answers

1,438 comments

35,551 users

Find the local maximum and minimum values of using both the First and Second Derivative Tests.

0 votes
 Find the local maximum and minimum values of  using both the First and Second Derivative Tests. Which  method do you prefer?
f (x) = 1 + 3x^2 - 2x^3.
asked Jan 22, 2015 in CALCULUS by anonymous
retagged Jan 22, 2015 by bradely

2 Answers

0 votes

Step 1:

The function

and

and

The critical points are and the test intervals are .

Step 2:

First derivative test:

Interval Test Value Sign of Conclusion
Decreasing
Increasing
Decreasing

is changes its sign from negative to positive, hence f  has a local minimum at .

Local minimum is 

is changes its sign from positive to negative, hence f  has a local maximum at

Local maximum is .

Solution:

Local minimum is  .

Local maximum is .

answered Jan 22, 2015 by david Expert
0 votes

Step 1:

The function

Second derivative test:

Differentiate with respect to image:

image

, curve is concave up, thus is a local minimum.

Local minimum is .

, curve is concave down, thus is a local minimum.

Local maximum is .

Solution:

Local minimum is  .

Local maximum is .

answered Jan 22, 2015 by david Expert

Related questions

...