Minimizing Triangle Area: Calculus Help for Line Equation at (1,4)

In summary, the formula for calculating the area of a triangle is A = 1/2 * b * h, where b is the base of the triangle and h is the height. To find the line equation at a given point, plug in the coordinates of the point for x and y and solve for m and b using the general equation for a line, y = mx + b. Yes, calculus can be used to minimize the area of a triangle, by taking the derivative of the area formula and setting it equal to 0, then solving for the value of b that minimizes the area. The point (1,4) represents the coordinates of one of the vertices of the triangle, and is significant in the context of minimizing
  • #1
Vandella
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0

Homework Statement



Find an equation of the line passing through the point (1, 4) such that the area of the triangle formed by this line and the positive coordinate axes is as small as possible.


Homework Equations





The Attempt at a Solution



No idea where to start this one please help
 
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  • #2
oops was not as hard as i first thought y=8-4x
 

1. What is the formula for calculating the area of a triangle?

The formula for calculating the area of a triangle is A = 1/2 * b * h, where b is the base of the triangle and h is the height.

2. How do I find the line equation at a given point?

The general equation for a line is y = mx + b, where m is the slope and b is the y-intercept. To find the line equation at a given point, plug in the coordinates of the point for x and y and solve for m and b.

3. Can calculus be used to minimize the area of a triangle?

Yes, calculus can be used to minimize the area of a triangle. This can be done by taking the derivative of the area formula and setting it equal to 0, then solving for the value of b that minimizes the area.

4. What is the significance of the point (1,4) in the context of minimizing triangle area?

The point (1,4) represents the coordinates of one of the vertices of the triangle. This point, along with two other points, forms a triangle that we are trying to minimize the area of using calculus.

5. Are there other methods besides calculus for minimizing triangle area?

Yes, there are other methods for minimizing triangle area, such as using geometry and trigonometry. However, calculus provides a more general and efficient approach for finding the minimum area of a triangle.

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