Max and min line equation

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In summary, the conversation discusses finding the equation of a straight line passing through a fixed point in the first quadrant such that the length of the segment that limits the positive semiaxes is minimal. The equation is determined by finding the slope and using the Pythagorean theorem to create a quartic equation. The solution is to set the slope to be equal to the negative cubic root of b/a.
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leprofece
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1) If P (a, b) is a fixed point located in the first quadrant. Find the equation of the straight line which, passing through P, is such that the length of the segment that on it limits the semiaxes positives is minimal. Calculate the segment lenght

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y-b = Cubic sqrt ((b)/a) (x-a)

L2/3 = a2/3 + b 2/3

Equation y-b = m(x-a)
According to the answer I must get the slope m derivating what?
 
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  • #2
Determine the $x$ and $y$ intercepts of the line, then find the square of the line segment as a function of $m$ using the Pythagorean theorem. Differentiating it produces an expression containing $m$, $1/m^2$ and $1/m^3$, i.e., essentially a quartic equation. It may be tricky to solve it, but it is easy to verify that $m=-\sqrt[3]{\dfrac{b}{a}}$ is root.
 

FAQ: Max and min line equation

What is the max and min line equation?

The max and min line equation is a mathematical formula used to determine the maximum and minimum values of a given set of data points. It is commonly used in statistics and data analysis to find the highest and lowest points on a graph or data set.

How is the max and min line equation calculated?

The equation is calculated by finding the slope of the line connecting the two highest data points and the slope of the line connecting the two lowest data points. The max line is then drawn by extending the line with the higher slope until it intersects with the x-axis, and the min line is drawn by extending the line with the lower slope until it intersects with the x-axis.

What is the significance of the max and min line equation?

The equation is useful for identifying extreme values in a data set, which can provide insights into the overall pattern and trends of the data. It can also help in identifying outliers or anomalies that may impact the overall analysis of the data.

What are some limitations of the max and min line equation?

The equation assumes a linear relationship between the data points and may not accurately represent the data if the relationship is not linear. It also does not take into account the distribution or frequency of the data points, which can affect the overall analysis.

Can the max and min line equation be used for non-numerical data?

No, the equation is only applicable to numerical data as it relies on the calculation of slopes and the intersection with the x-axis. It cannot be used for non-numerical data such as categorical or qualitative data.

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