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find the set of x-values where f(x) has point of inflection

0 votes
f(x)=e^(1-(x^2/18))

1.what is the domain of f(x)

2. find set of possible points of inflection using 2nd derivative

3.find the intervals on which f(x) is concave up

4.find the intervals on which f(x) is concave down

5. find the set of x-values where f(x) has point of inflection
asked Sep 9, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(1)

The function is image.

Domain:

The domain of a function is all values of , those makes the function mathematically correct.

The domain of exponential functions is all real numbers.

Therefore, the domain of image is all real numbers.

answered Sep 9, 2015 by Sammi Mentor
0 votes

(2)&(5)

Step 1:

The function is image.

Apply derivative on each side with respect to .

image

Apply formula:image.

image

image

image.

Again apply derivative on each side with respect to .

image

Apply product rule of derivatives image.

image

image

image

image

image

image.

Step 2:

Find the inflection points, by Equate to zero.

image

The exponential function can not be zero.

image.

image

image

image

image

image.

The inflection points at image.

Step 3:

Find the inflection point at image.

Substitute image in .

image

Find the inflection point at image.

Substitute image in .

image

The inflection points are image and image.

Solution:

(2): The inflection points are image and image.

(5): The set of -values where has point of inflections are image.

answered Sep 9, 2015 by Sammi Mentor
edited Sep 9, 2015 by casacop
0 votes

(3)&(4)

The point of inflections are at image.

The test intervals are imageimage and image.

Interval

Test Value Sign of Concavity
image image Up
image image

Down

image image image Up

The function is concave up on the intervals image and image.

The function is concave down on the interval image.

Solution:

(3): The function is concave up on the intervals image and image.

(4): The function is concave down on the interval image.

answered Sep 9, 2015 by Sammi Mentor

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