# Maths

posted by .

what is the max value of y=x^22/10x^logx

• Maths -

y = x^22 / 10x^logx
Nasty, but straightforward
Recall that d/dx (u^v) = v/u u^v u' + lnu u^v v'

I will assume by logx you mean lnx. If not, just recall that logx = lnx/ln10

d/dx x^lnx = (2/x lnx) x^lnx

So, using the quotient rule, we have

y' = 22x^21/(10x^logx) + x^22(20/x logx) x^logx
= 1/5 x^21/x^logx (11 - logx)

y'=0 when logx = 11, or x = e^11

y(e^11) = 1/10 e^121

whew - that's big!

## Similar Questions

1. ### college

FIND THE VERTEX THE LINE OF SYMMETRY THE MAX OR MIN VALUE OF THE FOLLOWING F(X)= -X^2+10X+5
2. ### math

I tried everthing but,I couldn't solve it. Please help me.the answer at the back is 40960.13 question: solve for x and check your solution. logx/log2 + logx/log4 + logx/log8 + logx/log16 = 25 THANK YOU FOR YOUR KIND HELP!!!!
3. ### ^Maths^

If Logx-6 base3=2y and Logx-7 base2=3y, show that x^2-13x+42=72y
4. ### Calculus

Demand Equation. The price(in dollars),and the quantity x sold of a certain product, obey the demand equation. I can't figure out what price the company should charge to maximize revenue p=-1/10x+150 R=p*x R=((-1/10)*x+150)*x R=(-1/10)*x^2+150x …
5. ### logarithms maths

logx+logx+n-logx/n.plz solve with explanation thanks
6. ### Maths

If logx^3=0.5,find the value of x.
7. ### value

Logx + logy=4 logx +2logy=3
8. ### maths need help log

if loxbase 2=k^2+2k what is the value of logx^3 base64
9. ### math algebra

Sum the following term of progression to the last term, logx, logx^2 logx^3.... logx^120
10. ### value

show that the sum of nterm of the progression is logx,logx^2,logx^3,logx^4---is n(n+1)/2 logx

More Similar Questions