Why can’t I do it like this(Q35) epo (a) Write the area A of theIMO cross as a function of xm and find the value of x thatusG co maximizes the area.i (b) Write the area A of the cross as a function of 0 and findpeb the value of 0 that maximizes the area. CEGLEXGLC(c) Show that the critical numbers of parts (a) and (b) yield thesame maximum area. What is that area?35. Minimum Distance Find the point on the graph of thepeun quationw 16x = yo vd bomol ai bilethat is closest to the point (6, 0).PUTNAM EXAM CHALLENGEod s36. Find, with explanation, the maximum value off(x) = xx* + 36 < 13x².- 3x on the set of all real numbers x satisfying37. Find the minimum value of(x + 1/x) - (x + 1/x) – 2(x + 1/x)3 + (x³ + 1/x)for x > 0.These problems were composed by the Committee on the Putnam PrizeCompetition. O The Mathematical Association of America. All rights reserved.= 2X-12416%3D%D

Name: Why can’t I do it like this(Q35) epo (a) Write the area A of theIMO cr
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: Why can’t I do it like this(Q35) epo (a) Write the area A of theIMO cross as a function of xm and find the value of x thatusG co maximizes the area.i (b) Write the area A of the cross as a function of 0 and findpeb the value of 0 that maximizes the a

Answered: 35. Minimum Distance Find the point on…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Why can’t I do it like this(Q35)

epo (a) Write the area A of the
IMO cross as a function of x
m and find the value of x that
usG co maximizes the area.
i (b) Write the area A of the cross as a function of 0 and find
peb the value of 0 that maximizes the area. CEGL
EXGLC
(c) Show that the critical numbers of parts (a) and (b) yield the
same maximum area. What is that area?
35. Minimum Distance Find the point on the graph of the
peun quation
w 16x = y
o vd bomol ai bile
that is closest to the point (6, 0).
PUTNAM EXAM CHALLENGE
od s
36. Find, with explanation, the maximum value of
f(x) = x
x* + 36 < 13x².
- 3x on the set of all real numbers x satisfying
37. Find the minimum value of
(x + 1/x) - (x + 1/x) – 2
(x + 1/x)3 + (x³ + 1/x)
for x > 0.
These problems were composed by the Committee on the Putnam Prize
Competition. O The Mathematical Association of America. All rights reserved.
= 2X-12416
%3D
%D

Expert Solution

Step 1

35. Given, equation of the graph is $16 x = y^{2}$ .

To find the point on the graph which is closest to the point (6,0).

To find that point, first arbitrarily take a point on the graph and find the distance between (6,0) and that point.

After that minimize that distance equation using second derivative test.

Step 2

To find the point:

Given equation of the graph $16 x = y^{2} \Rightarrow x = \frac{y^{2}}{16} . . . (1)$

Let $(x_{0}, y_{0})$ be a point on the curve .

Now the distance between two points $(x_{0}, y_{0})$ & (6,0) is,

Distance = $\sqrt{{(x_{0} - 6)}^{2} + {(y_{0} - 0)}^{2}}$

$= \sqrt{{(\frac{{y_{0}}^{2}}{16} - 6)}^{2} + {y_{0}}^{2}} = \sqrt{\frac{{y_{0}}^{4}}{256} - \frac{3}{4} {y_{0}}^{2} + {y_{0}}^{2} + 36} = \sqrt{\frac{{y_{0}}^{4}}{256} + \frac{1}{4} {y_{0}}^{2} + 36}$

Take $D = {(d i s \tan c e)}^{2} = \frac{{y_{0}}^{4}}{256} + \frac{{y_{0}}^{2}}{4} + 36$

Step by step

Solved in 3 steps

Knowledge Booster

$Angles, Arcs, and Chords and Tangents$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions