Answer:
f^-1 (x) = 1/2x - 4
Step-by-step explanation:
Use substitution: y = 2x + 8
x = 2y + 8
2y + 8 = x
2y = x - 8
y = 1/2x - 4
Then solve for your answer
Absolute maximum value for this expression is
.
What is absolute maximum ?
- The largest value that a mathematical function can have over its entire curve (see curve entry 3 sense 5a) .
- The absolute maximum on the graph occurs at x = d, and the absolute minimum of the graph occurs at x = a.— W.
f(x) = 2x³ - 4x² +2 , [ 1/2 , 1 ]
First critical points , by setting f'(x) = 0
f'(x) = d/dx ( 2x³ - 4x² + 2 )
= 6x² - 8x
Now 6x² - 8x = 0
2x( 3x - 4 ) = 0
2x = 0 or 3x-4 = 0
x = 0 , x = 4/3
Critical points x = 0 , x = 4/3
The critical points are not in the given interval [1/2, 1 ]
evaluate the function at the end points .
x = 1/2 ⇒ f(1/2) = 2(1/2)³ - 4( 1/2)² + 2
= 1/4 - 1 + 2
= 1/4 + 1
= 5 /4
x = 1 ⇒ f(1) = 2 (1)³ - 4(1)² +2
= 2 - 4 + 2 ⇒ 0
∴ absolute maximum = ![( \frac{1}{2} , \frac{5}{4} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B2%7D%20%2C%20%20%20%5Cfrac%7B5%7D%7B4%7D%20%20%29)
Learn more about absolute maximum
brainly.com/question/13774780
#SPJ4
<u>The complete question is - </u>
Given the function f left parenthesis x right parenthesis equals 2 x cubed minus 4 x squared plus 2; locate the absolute maximum point for this function on the interval open square brackets 1 half comma space 1 close square brackets. a. (1, 0) b. open parentheses 1 half comma space 5 over 4 close parentheses c. only (0, 2) d. open parentheses 2 over 3 comma space 22 over 27 close parentheses.
Answer:
It takes 10 fewer minutes for Noah than for Charlotte to home from school each day.
Step-by-step explanation:
We use the following relation to solve this question:
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
In which v is the velocity, d is the distance, and t is the time.
Finding the distance:
Charlotte walks home from school every day at a rate of 4 miles per hour. It takes her 30-minutes to reach home.
This means that
. Time is 0.5 because as the velocity is in miles per hour, the time has to be in hours. We use this to find d.
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![4 = \frac{d}{0.5}](https://tex.z-dn.net/?f=4%20%3D%20%5Cfrac%7Bd%7D%7B0.5%7D)
![d = 4*0.5 = 2](https://tex.z-dn.net/?f=d%20%3D%204%2A0.5%20%3D%202)
The distance is of 2 miles.
Her brother, Noah, runs home from the same school every day at a rate of 6 miles per hour.
We have to find t, in hours, for which
. So
![v = \frac{d}{t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
![6 = \frac{2}{t}](https://tex.z-dn.net/?f=6%20%3D%20%5Cfrac%7B2%7D%7Bt%7D)
![6t = 2](https://tex.z-dn.net/?f=6t%20%3D%202)
![t = \frac{1}{3}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
A third of an hour. In minutes, this is a third of 60, that is 60/3 = 20 minutes.
How many fewer minutes does it take Noah than Charlotte to reach home from school each day?
Noah: 20 minutes
Charlotte: 30 minutes
30 - 20 = 10
It takes 10 fewer minutes for Noah than for Charlotte to home from school each day.
Answer:
the sales tax is $1.80
Step-by-step explanation:
39.98*4.5%=1.7991
then you round up
$1.80
Sales after tax is
$41.78
you add 39.98+1.80