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Crank
3 years ago
7

Consider the function below. f(x) = ln(x4 + 27) (a) Find the interval of increase. (Enter your answer using interval notation.)

Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the interval where the graph is concave upward. (Enter your answer using interval notation.) Find the intervals where the graph is concave downward. (Enter your answer using interval notation.)
Mathematics
1 answer:
andrezito [222]3 years ago
6 0

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

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2 t-shirts and 3 hats costs £12.
Mariana [72]

Answer:

Cost of tshirt = £7.29

Cost of what = £0.86

Step-by-step explanation:

2t +3h = 12; 10t + 15h = 60

5t + 4h =33; 10t + 8h = 66

15h -8h = -6

7h = -6; h = -6/7; h = 0.86

2t +3(-6/7) =12

14t -18 = 84

14t = 102; t = 102/ 14; t=7.29

6 0
3 years ago
Giovanna and Janet have jobs where they get paid by the hour .Below are the numbers of hours of each have worked on each of the
Harman [31]
I would need more information to help you. Like the numbers of hours worked, amount of money made, and the statements.
5 0
3 years ago
5/3x-4/3x-1=8 solve please
SOVA2 [1]

Answer:x=27

Step-by-step explanation:

3 0
2 years ago
Use the distributive property to simplify the expression below:
Lorico [155]
4x + 2x + 2
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So the answer is B
8 0
3 years ago
Read 2 more answers
15
Evgesh-ka [11]

Answer:

Height = 14.4

Step-by-step explanation:

The diagonals meet at right angles. Interesting property.

The hypotenuse is the side of the rhombus = 15 cm

One of the sides of the small triangles created by the intersection of the diagonals = 24/2 = 12

You can find the other side of the the triangle by using the Pythagorean Theorem

a^2 + b^2 = c^2

c = 15

a = 12

b = ?

12^2 + b^2 = 15^2

144 + b^2 = 225

b^2 = 225 - 144

b^2 = 81

b = 9

The area of this right angle = 9 * 12/2 = 54

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That's the area of the rhombus.

The h= Area / b

b = 15

h = 216/15

h = 14.4

8 0
2 years ago
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