All categories

3 years ago

Consider f(x)=cos^2x+2cosx over one complete period beginning with x=0

1 answer:

3 0

Period is from 0 to 2pi

take the deritivive then take it again
we get f''(x)=-4cos²(x)-2cos(x)+2

it is negative between 0 and pi/3 and also between 5pi/3 and 2pi

concave down in the interval
$[0, \frac{ \pi }{3}]$ U $[\frac{ 5\pi }{3},2\pi]$

You might be interested in

two kilograms of ground cinnamon is packaged into bags containing 38 grams each.there will also be cinnamon left over.how many b

Fantom [35]

There will be 52 full bags plus an additional one that is not quite full yet.

7 0

4 years ago

This is my last question please help asap!!

Ivanshal [37]

The average rate of change of function $g(x)=5(2)^{x}$ from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

The correct option is (A).

What is the average rate of change of a function?

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

Using function notation, we can define the Average Rate of Change of a function f from a to b as:

$rate(m) = \frac{f(b)-f(a)}{b-a}$

The given function is $g(x) = 5(2)^{x}$ ,

Now calculating the average rate of change of function from x = 1 to x = 2.

$m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10$

Now, calculate the average rate of change of function from x = 3 to x = 4.

$m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40$

The jump from m = 10 to m = 40 is "times 4".

So option (A) is correct.

Hence, The average rate of change of function $g(x)=5(2)^{x}$ from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

To learn more about the average rate of change of function, visit:

brainly.com/question/24313700

#SPJ1

7 0

1 year ago

Solve for x <img src="https://tex.z-dn.net/?f=8%20%7B%7D%5E%7B2%20%2B%20x%7D%20%20%20%2B%202%20%7B%7D%5E%7B3x%7D%20%20%3D%203

Stella [2.4K]

Answer:

8^2+x + 2^ 3x = 32^ 1/2

2^3(2+x) + 2^3x = 2^5^1/2

All two's will cancel out

3(2+x) + 3x = 5^1/2

6+3x + 3x = 5^1/2

6 +6x = 2.23

6x = 2.23 - 6

6x = -3.77

x = -3.77÷ 6

x = -0.63

7 0

3 years ago

Lance bought 12 quarts of lemonade so that everyone who came to his party could have exactly 1/3 quart. How many people did Lanc

igor_vitrenko [27]

Lance invited 36 people to his party.

Step-by-step explanation:

It is given that,

Lance bought 12 quarts of lemonade.
Everyone who came to his party could have exactly 1/3 quart.

We know that,

The total quarts of lemonade available for the party = 12

Each person in the party consumes = 1/3 quart.

We need to find out how many people did Lance invited to his party.

To find the number of people :

Let us consider 'x' be the number of people invited to the party.

Total lemonade = number of people × lemonade for each person.

⇒ 12 = x × 1/3

⇒ 12×3 = x

⇒ x = 36 people

Therefore, Lance invited 36 people to his party.

6 0

3 years ago

A toy store sells assorted bags of marbles sold in small or large bags the table show the number of each color of marble in the

Sidana [21]

Answer:

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers