onsider the equation below. (If an answer does not exist, enter DNE.) f(x) = 8 cos2(x) − 16 sin(x), 0 ≤ x ≤ 2π (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) (No Response) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (No Response) (b) Find the local minimum and maximum values of f. local minimum value (No Response) local maximum value (No Response) (c) Find the inflection points. (x, y) = (No Response) (smaller x-value) (x, y) = (No Response) (larger x-value)

(a) Increasing: and Decreasing:

(b) The local minimum and maximum values are -16 and 16 respectively.

(c) The inflection points are

Step-by-step explanation:

The function provided is:

(a)

Then,

Note,

Then, for .

Also .

Thus, f (x) is increasing for,

And f (x) is decreasing for,

(b)

From part (a) f (x) changes from decreasing to increasing at and from increasing  to decreasing at .

The local minimum value is:

The local maximum value is:

(c)

Compute the value of f'' (x) as follows:

So,

And,

Thus, f (x) is concave upward on and concave downward on .

If , then f (x) will be:

If , then f (x) will be:

The inflection points are .

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

b. 2 and 4

step-by-step explanation: