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

Question

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

Answer 1

(1)

The function is .

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 is all real numbers.

Answer 2

(2)&(5)

Step 1:

The function is .

Apply derivative on each side with respect to .

Apply formula:.

.

Again apply derivative on each side with respect to .

Apply product rule of derivatives .

.

Step 2:

Find the inflection points, by Equate to zero.

The exponential function can not be zero.

.

.

The inflection points at .

Step 3:

Find the inflection point at .

Substitute in .

Find the inflection point at .

Substitute in .

The inflection points are and .

Solution:

(2): The inflection points are and .

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

Answer 3

(3)&(4)

The point of inflections are at .

The test intervals are ,  and .

Interval	Test Value	Sign of	Concavity
			Up
			Down
			Up

The function is concave up on the intervals and .

The function is concave down on the interval .

Solution:

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

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