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How do you find out the x-coordinates of the stationary points on the curve y equals (3x plus 1)caret5(3-x)caret3?
y = (3x + 1)⁵(3 - x)³
The stationary points are where dy/dx = 0
Note the use of:
If u and v are functions of x:
d/dx (uv) = v du/dx + u dv/dx
d/dx uⁿ = n uⁿ⁻¹ du/dx
dy/dx = (3 - x)³ d/dx (3x + 1)⁵ + (3x + 1)⁵ d/dx (3 - x)³
= (3 - x)³ 5 (3x + 1)⁴ d/dx (3x + 1) + (3x + 1)⁵ 3 (3 - x)² d/dx (3 - x)
= 5 (3 - x)³ (3x + 1)⁴ 3 + 3 (3x + 1)⁵ (3 - x)² (-1)
= 3 (3x + 1)⁴ (3 - x)² (5 (3 - x) - (3x + 1))
= 3 (3x + 1)⁴ (3 - x)² (15 - 5x - 3x - 1)
= 3 (3x + 1)⁴ (3 - x)² (14 - 8x)
= 6 (3x + 1)⁴ (3 - x)² (7 - 4x)
→ 3x + 1 = 0 → x = -1/3
or 3 - x = 0 → x = 3
or 7 - 4x = 0 → x = 7/4
What else can I help you with?
What points are on the line given by the equation y equals x?
Y Equals X PointsAll points that has the same y coordinates as x coordinates are on the y=x line.
How many points equals one vertical inch in a document?
I believe it is 72 points. 95 percent sure.
How do you divide 9 and 4?
It goes into decimal points, it equals 2.25
3 equals P in a T?
3 equal points in a triangle??
What is the answer to 624 points in 6 minutes how many points per minute?
5252
How stationary wave are produce?
Stationary waves are formed by the interference of two waves with the same frequency and amplitude traveling in opposite directions. This causes certain points along the medium to have nodes (points of no displacement) and antinodes (points of maximum displacement), creating a pattern of stationary nodes and antinodes that do not move but appear to oscillate.
Explain why reference points that are stationary are usually chosen to determine whether an object is in motion?
Stationary reference points are chosen to determine motion because they provide a consistent and fixed frame of reference. By using stationary reference points, it is easier to identify when an object is moving relative to its surroundings. This helps in accurately measuring the speed and direction of the object's motion.
What is the carat value of 5 points?
Five points equals .5 carats where one carat equals 1.00 points.
How stationary waves are formed?
Stationary waves are formed when two waves of equal amplitude and frequency traveling in opposite directions interfere with each other. This causes certain points, called nodes and anti-nodes, to appear stationary while other points continue to vibrate. The interference pattern creates a standing wave pattern that appears to be stationary.
Abc is a triangle in which points p and r are such that ap equals pr equals rb also points q and s are on ac such that aq equals qs equals sc show that 3pq equals bc?
Abc is a triangle in which points p and r are such that ap equals pr equals rb also points q and s are on ac such that aq equals qs equals sc show that 3pq equals bc?
What are 3 examples of reference points that are stationary relative to earth?
Motion movement and changes
Why reference points that are stationary are usually chosen to determine whether an object is in motion?
To support you in specifying how the reference point is placed and how the object is moved away from the reference point.
What are examples of reference points?
A reference point is anything that is stationary. So, if you are on a train you know you have left the station because you moved away from the platform. Hence the platform was stationary.
Twice as many points as bob would be 18 points?
If twice as many points as Bob equals 18 points, then Bob must have 9 points. This is because 18 divided by 2 equals 9. Therefore, Bob has 9 points.
What is a wave that forms a stationary pattern in which portions of the wave do not move and other portions move with large amplitude?
This type of wave is called a standing wave. It is created by the interference of two waves of the same frequency and amplitude traveling in opposite directions. The points where the wave appears to be stationary are called nodes, while the points with the largest amplitudes are called antinodes.
Which type of wave has points called nodes that do not move?
Standing waves have points called nodes that do not move. These nodes are points of zero amplitude where the two interfering waves cancel each other out.
What does stationary math mean?
Stationary math refers to mathematical concepts and techniques that deal with systems or processes that do not change over time. In the context of calculus, it often involves analyzing stationary points, where the derivative of a function is zero, indicating potential maxima, minima, or points of inflection. This concept is crucial in optimization problems and in understanding the behavior of functions. Essentially, it focuses on conditions where variables remain constant or stable.
