Please Help Fast Algebra 1
1 answer:
Answer:
The answer is B.
Step-by-step explanation:
The question ask us to find an equation for the cost of a fill-up and a car wash. Firstly, we have to form 2 coordinates from the table and find the gradient :
Let Tank Size be x and Total Cost be y,
Any 2 coordinates,
Let (11,21.45) be (x1,y1) & (15,28.25) be (x2,y2),
m = (28.25-21.45)/(15-11)
= 6.8/4
= 1.7
You can form equation using slope-form, y = mx+b, then substitute m value and any coordinates into the equation :
Let m= 1.7 & (17,31.65),
y = mx + b
31.65 = 1.7(17) + b
31.65 - 1.7(17) = b
b = 2.75
y = 1.7x + 2.75
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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)
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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