Math Project Part 3.doc - Introduction This is the Part III of the math project in this part we deal with no only f(x but also f ’(x and f ’’(x

Math Project Part 3.doc - Introduction This is the Part III...

This preview shows page 1 - 4 out of 25 pages.

Introduction: This is the Part III of the math project; in this part, we deal with no only f(x), but also f ’(x) and f ’’(x). f(x) helps find the elevation of any point along the line, f ’(x) helps find the slope at any point of the line, and f ’’(x) tells you the concavity of the line in our project. In this project, first we find the first and second deveriative of the A(x), B(x), and C(x) in the piecewise function. Then we do the midpoint analysis and random point analysis using theses deveriatives. In the function breakdown, for every function, we’ll find the critical points using the first deveriative, and the point of inflection using the second deveriative. For the power, exponential, and logarithmic function, however, we’ll prove that these functions have no critical point and point of infection, and then using the first and second deveriative, we’ll plug in a random x-value to find if the line is increasing or decreasing, and the concavity of the function.
Image of page 1
Piecewise function for A(x) .0190353867x 2 - .6133526137x + 53.44611511 .1 ≤ x < 47 (1) 60.06101939(1.002216961) x 47 ≤ x < 95 (2) A(x)= 56698.74303x -1.475707031 95 ≤ x < 173 (3) 1.180637442 E 17x -6. 9681296 173 ≤ x < 185 (4) -.08833x + 36.406856 185 ≤ x 237 (5) .03807077x - .6133526137 .1 ≤ x < 47 (1) .133005558(1.002216961) x 47 ≤ x < 95 (2) A’(x)= -83630.64597x -2.475 95 ≤ x < 173 (3) -8.22683471 E 17x -7.9681296 173 ≤ x < 185 (4) -.08833 185 ≤ x < 237 (5) .03807077 .1 ≤ x < 47 (1) 2.945417615 E -4(1.002216961) x 47 ≤ x < 95 (2) A’’(x) 206985.8488x -3.475 95 ≤ x < 173 (3) 6.555248517 E 18x -8.9681296 173 ≤ x < 185 (4) 0 185 ≤ x < 237 (5) A(x) evaluates the elevation, in feet, above sea level, at any point between 65 th Street Park Avenue and intersection of Spring Street Hudson Street. A’(x) evaluates the slope, in ft/mm at any point between 65 th Street Park Avenue and intersection of Spring Street Hudson Street. A’’(x) evaluates the concavity of the land in ft/mm 2 at any point between 65 th Street Park Avenue and intersection of Spring Street Hudson Street. 2
Image of page 2
x represents the number of millimeter away from 65 th Street Park Avenue toward intersection of Spring Street Hudson Street, which is included with the project. Midpoint analysis 1) The midpoint at 65 th Street Park Avenue and intersection of Spring Street Hudson Street is located on 29 th Street between 5 th Avenue and Madison Avenue on my map. It is obtained from Part I of the project. 2) The corresponding x-value at the midpoint is 118.5mm, since the whole distance of A(x) is 237mm, 237/2 = 118.5mm. 3) The elevation for the midpoint is 52.6019ft above sea level. The elevation is obtained by Part II of this project. 4) The slope for the midpoint is –40.6870728ft/mile, which means if I continue with the exact slope, I will evaluate –40.6870728ft vertically for every 1 mile. Plus since the slope is negative, I will be walking downhill. Work: A’(x) = -83638.64597x -2.475 A’(118.5) = -83638.64597(118.5) -2.475 A’(118.5) = -.6164708ft -.6164708ft 66mm = -40.6870728ft = -40.6870728ft/mile 1mm 1mile 1mile 66mm/1miles is the standard unit for the map project, it means that 66mm in our map project equal 1 mile in real life length.
Image of page 3
Image of page 4

You've reached the end of your free preview.

Want to read all 25 pages?

  • Spring '14
  • DanielMcKinney

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes