The given polynomial function has 1 relative minimum and 1 relative maximum.
<h3>What are the relative minimum and relative maximum?</h3>
- The relative minimum is the point on the graph where the y-coordinate has the minimum value.
- The relative maximum is the point on the graph where the y-coordinate has the maximum value.
- To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)
<h3>Calculation:</h3>
The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
Learn more about the relative minimum and maximum here:
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Answer:
<h2>PART A: x = 15 and y = -8</h2><h2>PART B: x = -5 and y = 3</h2>
Step-by-step explanation:
PART A:
The first equation is 
The second equation is 
Putting the value of y from (a) in the above equation, we get 
From (a) we get y = 7 - x = 7 - 15 = -8
PART B:
Here the system of equations are 
From (a) we get, 
Putting the above value of x in (b) we get, 
Hence, 
Answer
im only in year 9 do you expect me to know that ????????????????????????????
Y+4<u><</u>9
subtract 4
y<u><</u>5
y is smaller than and equal to 5
so you shade from 5 to the negative end to infinity (to the left) and shade the 5 to show that it is included (attachment says A)
6 less than (-6) 2 times a number (2 time x) is greater than (>) 8 (8)
-6+2x>8
add 6
2x>14
divide 2
x>7
so
x is bigger than 7
shade from 7 to the positive end to infinity (to the right) and don't shade 7 but put a circle around it to show that it is not included (attachment says B )
I have included pictures of the number lines
I’m sorry this isn’t an answer but what in the world are y’all learning what is this ?! i’m in high school & i don’t know this