Maximizing the area of a triangle

  • Context: MHB 
  • Thread starter Thread starter markosheehan
  • Start date Start date
  • Tags Tags
    Area Triangle
Click For Summary
SUMMARY

The forum discussion centers on maximizing the area of a triangle formed by points on the graph of the function y = x². The specific problem referenced is #25, which requires finding the value of x that maximizes the triangle's area. The incorrect formula provided initially was √x² + √16/x². Participants emphasize the importance of clear problem statements and proper formatting in forum posts to facilitate better assistance.

PREREQUISITES
  • Understanding of calculus principles, particularly related to optimization.
  • Familiarity with the area formula for triangles.
  • Knowledge of graphing quadratic functions, specifically y = x².
  • Ability to interpret and analyze mathematical problems presented in written form.
NEXT STEPS
  • Study optimization techniques in calculus, focusing on critical points and maximum values.
  • Review the area formula for triangles and its application in coordinate geometry.
  • Practice problems involving quadratic functions and their graphical representations.
  • Learn effective communication strategies for presenting mathematical problems in forums.
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in improving their problem-solving skills related to geometry and optimization.

markosheehan
Messages
133
Reaction score
0
View attachment 5904

can some1 show me how to do this the answer to the first part is √x²+√16/x²
 

Attachments

  • WIN_20160821_11_13_34_Pro.jpg
    WIN_20160821_11_13_34_Pro.jpg
    67.6 KB · Views: 107
Physics news on Phys.org
Re: calculus

"
markosheehan said:
can some1 show me how to do this the answer to the first part is √x²+√16/x²

"The first part" of what? The only problem that is really clear is #26 where the first part asks you to "find the coordinates of point C". The answer to that is certainly not "√x²+√16/x²"!

So you are referring to #25? You are given the graph of y= x^2 and three points on that graph, (-2, 4), (4, 16), and (x, x^2). The lines connecting those points are drawn to form a triangle. The "first part" of #25 asks you to Find the value of x such that this triangle has maximum area.

Ok, what formulas do you know for calculating the area of a triangle? Which of those could you use here?
 
I have edited the thread title to briefly describe the problem. A thread title of "calculus" for a thread posted in our "Calculus" forum gives no additional information about the question being asked.

When attaching images of problems, it is better to hold your camera so that the lens is parallel to the sheet of paper and then crop the image so that only the problem about which you are asking is in the image. This makes it easier for our helpers to interpret the image and the question being asked.

Also, please refrain from "textspeak" in the body of your post. Go ahead and type "someone" instead of "some1" for improved readability (it's only 2 additional keystrokes and looks so much better). :D

I don't mean to be a grumpy ol' meanie, it's just that these are things that help make MHB more useful for everyone.
 
ok and ye the back of the book shows the answers and it must be wrong i worked it out anyway
 

Similar threads

Undergrad Help with area formula using direction cosines
  • · Replies 3 ·
Replies
3
Views
2K
Find the limit of the sum of the areas of all these triangles
  • · Replies 7 ·
Replies
7
Views
1K
MHB 12.4.9 - Area of a triangle given points in 3D space
  • · Replies 5 ·
Replies
5
Views
3K
MHB What Is the Minimum Surface Area for a Cuboid Box with a Square Base?
  • · Replies 4 ·
Replies
4
Views
2K
High School Calculating shaded area: I'm getting discrepancies between methods
  • · Replies 3 ·
Replies
3
Views
3K
High School Question about units for "area under curve"
  • · Replies 2 ·
Replies
2
Views
3K
MHB Find Area of Triangle with Vertices $(0, 0, 0), (1, 1, 1)$ and $(0, -2, 3)$
  • · Replies 4 ·
Replies
4
Views
2K
High School Area Increasing as a linear dimension increases -- Looking for intuition on this
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Area distribution of inscribed triangles in a circumference
  • · Replies 12 ·
Replies
12
Views
3K
Finding area of a non right angled triangle
  • · Replies 9 ·
Replies
9
Views
4K