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[ (a-b) 2 + (a 2 /20 - { (17-b)x(b-13) } 1/2 ) 2 ] a, b are variables (like usually used x.) can you tell me how to find the minimum value of the above expression and for what values of a and b will it be maximum......... please help. ...

[(a-b)2 + (a2/20 - { (17-b)x(b-13) }1/2 )2]


a, b are variables (like usually used x.)


can you tell me how to find the minimum value of the above expression and for what values of a and b will it be maximum.........


please help....

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
f(a, b) = (a-b)^{2}+(\frac{a^{2}}{20}-\sqrt{(17-b).(b-13)})^{2}
f(a, b) = a^{2} + \frac{a^{4}}{400}-2ab-\frac{a^{2}}{10}.\sqrt{(17-b).(b-13)}+ ((17-b).(b-13))13\leq b\leq 17
\frac{\partial f(a, b)}{\partial a} =2a + \frac{a^{3}}{100}-2b-\frac{a}{5}\sqrt{(17-b)(b-13)} = 0
From here, you will get the value of a in the form of b.
Put that value in the equation & you will get the equation in b.
Then differentiate the function w.r.t b & equate it to zero.
Calculate b from the equation & select appropriate from the value b/w 13 & 17 for maxima & minima.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
Matt Farrel
12 Points
6 years ago
Can you explain how to get a in form of b from last equation.

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