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Juli2301 [7.4K]
3 years ago
12

Determine the location and values of the absolute maximum and absolute minimum for given function : f(x)=(‐x+2)4,where 0<×&lt

;3
Mathematics
1 answer:
brilliants [131]3 years ago
5 0

Answer:

Where 0 < x < 3

The location of the local minimum, is (2, 0)

The location of the local maximum is at (0, 16)

Step-by-step explanation:

The given function is f(x) = (x + 2)⁴

The range of the minimum = 0 < x < 3

At a local minimum/maximum values, we have;

f'(x) = \dfrac{(-x + 2)^4}{dx}  = -4 \cdot (-x + 2)^3 = 0

∴ (-x + 2)³ = 0

x = 2

f''(x) = \dfrac{ -4 \cdot (-x + 2)^3}{dx}  = -12 \cdot (-x + 2)^2

When x = 2, f''(2) = -12×(-2 + 2)² = 0 which gives a local minimum at x = 2

We have, f(2) = (-2 + 2)⁴ = 0

The location of the local minimum, is (2, 0)

Given that the minimum of the function is at x = 2, and the function is (-x + 2)⁴, the absolute local maximum will be at the maximum value of (-x + 2) for 0 < x < 3

When x = 0, -x + 2 = 0 + 2 = 2

Similarly, we have;

-x + 2 = 1, when x = 1

-x + 2 = 0, when x = 2

-x + 2 = -1, when x = 3

Therefore, the maximum value of -x + 2, is at x = 0 and the maximum value of the function where 0 < x < 3, is (0 + 2)⁴ = 16

The location of the local maximum is at (0, 16).

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(8, 1) and (-1, 10)<br> Slope
gizmo_the_mogwai [7]

Answer:

<h2>The answer is 1</h2>

Step-by-step explanation:

The slope of the line between two points can be found by using the formula

m =  \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}

where

(x1 , y1) and (x2 , y2) are the points

From the question is points are

(8, 1) and (-1, 10)

Substitute the values into the above formula and solve for the slope

That's

m =  \frac{10 - 1}{8 + 1}  \\  =  \frac{9}{9}   = 1

We have the final answer as

<h3>1 </h3>

Hope this helps you

7 0
3 years ago
Chris has 35 cookies for the bake sale. The ratio of chocolate chip coskies to peanut butter is 4:3. How many chocolate chip coo
Olin [163]
20 chocolate chip, 15 peanut butter. I don't know how to show that on a diagram, but this can at least get you started
8 0
3 years ago
Graph (1,1), (1,2), (1,3), (1,4)
jenyasd209 [6]

Answer:

There is not a way that I can show you how to graph it, so I will try and explain it.

Step-by-step explanation:

(1,1)

^  ^     y-axis

x-axis

You are just going right however many, and then up however many it says.

So if it's (1,1) you will go right one space, and then up one space.

Once you have all of your points on the graph, you put a line through them.

Hope this helps! :)

3 0
3 years ago
Rich deposited money into a bank account that earned 2.5% simple interest each year. After 2 years, he had earned $14.65 in inte
photoshop1234 [79]

we know that


The simple interest formula is equal to


I=Prt


where


P is the Principal amount of money to be invested


I is the amount of money in interest

r is the rate of interest  

t is Number of Time Periods


in this problem we have


t=2\ years\\ I=\$14.65\\r=0.025


substitute in the formula above  and solve for P

14.65=P(0.025)(2)

P=14.65/[(0.025)(2)]

P=\$293


therefore

<u>the answer is</u>

\$293




5 0
3 years ago
Read 2 more answers
A TV has a listed price of $695.95 before tax. If the sales tax rate is 7.75%, find the total cost of the TV with sales tax incl
Brut [27]

Answer:

$749.89

Step-by-step explanation:

TV price = 100% = 695.95

Sales TAX = 7.75% = x

Total price = 107.75% = x dollars

1.0775 * 685.95 = 749.886125 ≈ 749.89

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

5 0
3 years ago
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