Minimum value of the function, Mathematics

Assignment Help:

How the property AM>or = GM used to get minimum value of the function......e,g for what condition of a and b does minimum value of a tan^2 x + b cot^2 x equals maximum value of a sin^2 x + b cos^2x

Ans) for min value of first func. we have..AM>or=GM

i.e      a.tan^2x  + b.cot^2x >or = 2(a.tan2x.bcot2x)^1/2    .....[ a+b/2 .or= (ab)^1/2 ]
                                                   = 2(ab)^1/2
hence min value of first function is 2(ab)^1/2

for second func.
its in the form of a.siny + b.cosy whose max value =(a^2 + b^2)^1/2
applying this we get the max. value of the func. as= (a^2 + b^2)^1/2

hence req. condition=> 2(ab)^1/2=(a^2 + b^2)^1/2
                                => 4ab = a^2 + b^2
                                =>  a^2 + b^2 -  4ab=0  (ANS)

 


Related Discussions:- Minimum value of the function

Rounding, what is the nearest ten thousand of 92,892?

what is the nearest ten thousand of 92,892?

Find the discount factors -linear interpolation, Find the discount factors ...

Find the discount factors -Linear interpolation: All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765

5, what is a variable

what is a variable

Logorithms, log base 5 (3-2x) + log base 5 (2+x) = 1

log base 5 (3-2x) + log base 5 (2+x) = 1

Erp for a company, recomendation to a company to implement ERP to succeed

recomendation to a company to implement ERP to succeed

If 6 more black balls are put in the box find x, A box contains 12 balls ou...

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put i

Asymtotes, vwertical and horizontal

vwertical and horizontal

Example of subtraction of fractions, Example of Subtraction of Fractions: ...

Example of Subtraction of Fractions: 1/3 + 1/6 + 1/8 = ____ Using trial & error we could search that 24 is the LCD or smallest number in which 3, 6, and 8 will all divide w

Greatest common factors, Lindy has 48 chocolate chip cookies and 64 vanilla...

Lindy has 48 chocolate chip cookies and 64 vanilla wafers. How many bags can lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bags? She plans

Determine the taylor series, Example : Determine the Taylor series for f(x)...

Example : Determine the Taylor series for f(x) = e x about x=0. Solution It is probably one of the easiest functions to get the Taylor series for. We just require recallin

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd