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frutty [35]
3 years ago
7

12. A store charges a restocking fee for any returned item based upon the

Mathematics
1 answer:
bekas [8.4K]3 years ago
4 0
B b b b b b b b b b b b b b b b b b
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Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (E
xxTIMURxx [149]

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at <em>x = -3</em> and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

6 0
3 years ago
QUESTION 60 What is the mean of the following set of data? Round your answer to two decimal places. {25, 32, 16, 21, 30, 18, 37}
padilas [110]

Question 60:

The answer is B. 25.57.

Mean is calculated by adding up all the values of a data set, and then dividing that sum by the amount of values.

25, 32, 16, 21, 30, 18, 37=179

179÷7=25.57

Question 61:

The answer is A. 102.

Mode is the number in a data set that appears most often. 102 shows up twice, while the other values only appear once. So 102 is the mode.

3 0
3 years ago
Read 2 more answers
What is 6+2-8? make sure u give my my asnwer
yanalaym [24]

Answer: 0

Step-by-step explanation: 8-8 equals... ZERO GOOD JOB GUYS!

7 0
3 years ago
Read 2 more answers
If a = 5 in the right triangle what is the value of b and c
Nadya [2.5K]

Answer:

b=5√3, c=10

Step-by-step explanation:

30-60-90 triangle

c=2a

b=a√3

6 0
3 years ago
The circles are identical. What is the circumference of each circle? Circle 1: radius of 2x; Circle 2: diameter of 2x+3. A. 3/2
Delicious77 [7]

Answer:

C=6π

Step-by-step explanation:

It is given that, two circles are identical. The radius of first circle is 2x and the diameter of other circle is 2x+3.

If identical, it means that the radius of both circles are same i.e.

2x=\dfrac{2x+3}{2}\ \ (\because\ r=\dfrac{D}{2}, d=\text{diameter})\\\\4x=2x+3\\\\2x=3\\\\x=1.5

Radius of both circles is 2(1.5)=3

The circumference of a circle is given by :

C=2\pi r\\\\C=2\pi (3)\\\\C=6\pi

So, the circumference of each circle is 6π.

7 0
3 years ago
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