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
30min / 10 miles = 3min per mile
12 miles × 3min = 36 min to the ball park
Answer:
The internal diameter of the sphere is 6 cm.
Step-by-step explanation:
Given that, a solid right circular cone of diameter 14 cm and height 8 cm.
The radius of the cone is 

= 7 cm.
The volume of the cone is 

Let the internal radius of the sphere be r.
The external diameter of the sphere is = 10 cm
The external radius of the sphere is(R) = 5 cm
The volume of the sphere is 

The sphere is formed by the solid right circular cone.
∴The volume of the sphere = The volume of the cone
According to the problem,






⇒r= 3
The internal radius of the sphere is = 3 cm.
The internal diameter of the given sphere is = (2×3) cm =6 cm.
if segments OX = OC and perpendicular to those chords, then AB = YZ, the chords are also equal.