1800-150-456-789
FlagBACK
Flag Differential Calculus> finding the minimum value of an expressio...
question mark

[(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....

jatin parekh , 14 Years ago
Grade 12
anser 2 Answers
Jitender Singh

Last Activity: 10 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

Last Activity: 10 Years ago

Can you explain how to get a in form of b from last equation.

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on differential calculus

question mark
the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to  move once over to level a playground. find the area of the playground in square m?
differential calculus
1 Answer Available

Last Activity: 2 Years ago

question mark
Find dy/DX when y=x^sinx+sin-1√x.
 
Please give me the solution of this problem. 
differential calculus
0 Answer Available

Last Activity: 2 Years ago

question mark
If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.
differential calculus
0 Answer Available

Last Activity: 2 Years ago

question mark
Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.
differential calculus
0 Answer Available

Last Activity: 3 Years ago

question mark
Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.
differential calculus
0 Answer Available

Last Activity: 3 Years ago