maximum value

MATHEMATICIAN · April 18th, 2014, 09:35 AM

find the condition for maximum value for y.

y = sin arc (x sin r1) + sin arc (x sin r2)

also, r1 + r2 = K (constant)

MATHEMATICIAN · April 19th, 2014, 12:15 AM

i didnt know how to edit this post.

i am looking for the MINIMUM value instead of MAXIMUM.

v8archie · April 19th, 2014, 09:03 AM

It doesn't make a lot of difference. You need to differentiate wrt x. Can you do that?

I had a quick go at home, but I can't really see the point of the second equation (unless the $r_i$ are supposed to be functions of x. But even then, it looks a bit nasty to me.

MATHEMATICIAN · April 19th, 2014, 09:19 AM

sorry i could not differentiate it.

first differentiation = 0
second differentiation > 0 (for minimum)

i should differentiate y with respect to r1 or r2 ?

MATHEMATICIAN · April 19th, 2014, 09:20 AM

i forgot to mention,

x = constant

April 18th, 2014, 09:35 AM	#1
MATHEMATICIAN Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 390 Thanks: 32 Math Focus: Elementary Mathematics	maximum value find the condition for maximum value for y. y = sin arc (x sin r1) + sin arc (x sin r2) also, r1 + r2 = K (constant)
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April 19th, 2014, 12:15 AM	#2
MATHEMATICIAN Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 390 Thanks: 32 Math Focus: Elementary Mathematics	edit i didnt know how to edit this post. i am looking for the MINIMUM value instead of MAXIMUM.
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April 19th, 2014, 09:03 AM	#3
v8archie Math Team Joined: Dec 2013 From: Colombia Posts: 6,778 Thanks: 2195 Math Focus: Mainly analysis and algebra	It doesn't make a lot of difference. You need to differentiate wrt x. Can you do that? I had a quick go at home, but I can't really see the point of the second equation (unless the $r_i$ are supposed to be functions of x. But even then, it looks a bit nasty to me.
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April 19th, 2014, 09:19 AM	#4
MATHEMATICIAN Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 390 Thanks: 32 Math Focus: Elementary Mathematics	sorry i could not differentiate it. first differentiation = 0 second differentiation > 0 (for minimum) i should differentiate y with respect to r1 or r2 ?
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April 19th, 2014, 09:20 AM	#5
MATHEMATICIAN Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 390 Thanks: 32 Math Focus: Elementary Mathematics	i forgot to mention, x = constant
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