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## Homework Statement

Consider the function below. (Round the answers to two decimal places. If you need to use - or , enter -INFINITY or INFINITY.)

f(θ) = 2cos(θ) + (cos (θ))^2

0 ≤ θ ≤ 2π

(a) Find the interval of increase.

( , )

Find the interval of decrease.

( , )

(b) Find the local minimum value.

(c) Find the inflection points.

( , ) (smaller x value)

( , ) (larger x value)

Find the interval where the function is concave up.

( , )

Find the intervals where the function is concave down. (Enter the interval that contains smaller numbers first.)

( , ) ( , )

## Homework Equations

f(θ) = 2cos(θ) + (cos (θ))2

0 ≤ θ ≤ 2π

## The Attempt at a Solution

I tried using sign analysis with the second derivative (I definitely know that you have to use the second derivative) and all of the values for it. Thus:

_____________-2sinx 1 + cosx f'(x) f(x)

0 = 0

0 < x < pi/2

x = pi/2

pi/2 < x < pi

x = pi

pi < x < 3pi/2

x = 3pi/2

3pi/2 < x < 2pi

x = 2 pi

But I honestly don't know where to go from there

## Homework Statement

Consider the function below. (Give your answers correct to two decimal places. If you need to use - or , enter -INFINITY or INFINITY.)

f(x) = e^[-1/(x + 2)]

(c) Find the inflection point.

( , )

Find the intervals where the function is concave up.

( , ) ( , )

## Homework Equations

f(x) = e^[-1/(x + 2)]

## The Attempt at a Solution

I tried something similar to the above question