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:
brainly.com/question/9839310
#SPJ1
Answer:=6x3−9c
Step-by-step explanation:
3x3+4x2+3x3−4x2−9c
=3x3+4x2+3x3+−4x2+−9c
Combine Like Terms:
=3x3+4x2+3x3+−4x2+−9c
=(3x3+3x3)+(4x2+−4x2)+(−9c)
=6x3+−9c
7x+9
5x+2x= 7x
5+4=9
7x + 9 is the result when combining like terms.
Answer:
I cant graph it on yours, but hope this helps
Step-by-step explanation:
Answer:
number of cans Raina will be needed in court floor is 14 cans
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW;
Raina is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will she need to cover the court?
CALCULATION;
Given:
length of the rectangular shape =46 feet
width of the the rectangular shape = 35 feet.
The floor of the court room is having a rectangular shape, then we need to calculate the surface Area of the rectangular shape first in order to know the number of cans that Raina will be needed
Surface Area= Length × Width
= 46feet × 35 feet
=1610 square ft
Then to get the number of cans , we need to divide the surface Area by each can of wood stain covers which is 115 square feet,
number of cans Raina will be needed in court = 1610 square ft / 115 square ft = 14
number of cans Raina will be needed in court floor is 14cans
