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If x,y are strictly positive such that x...

If x,y are strictly positive such that x+y=1 then the minimum value of xlogx+ylogy is

A

log 2

B

`-log 2`

C

2 log 2

D

0

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-APPLICATIONS OF DIFFERENTIATION-EXERCISE 1E (MAXIMA AND MINIMA)
  1. If x is real, then the minimum value of y=(x^(2)-x+1)/(x^(2)+x+1) is

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  2. if x is real , the maximum value of (3x^2+9x+17)/(3x^2+9x+7) is

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  3. If x,y are strictly positive such that x+y=1 then the minimum value of...

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  4. If l^(2)+m^(2)=1 then the max value of l+m is

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  5. If x is real and (a sin x +b cos x)/(c sin x +d cos x) has neither max...

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  6. The greatest value of the function f(x) =sin 2x -x on [-pi//2,pi//2] ...

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  7. The least value of f(x) = sin 2x -x on [-pi//2,pi//2] is

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  8. The difference between the greatest and least value of the function f(...

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  9. For a gt 0, if the function f(x)=2 x^(3) - 9 a x^(2) + 12 a^(2) x + 1...

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  10. If ma and M respectively denote the minimum and maximum of f(x) =(x-1)...

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  11. Let f : R to R be defined, by {{:(k-2x,"if"" "x le -1),(2x+3,"if" " "...

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  12. p and q are distinct prime numbers and if the equation x^2 -px ...

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  13. Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d such that x=0 is the only real ro...

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  14. A curve passes through the point (2,0) and the lope of the tangent at ...

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  15. The point on the curve y=x/(1+x^2) where the tangent to the curve has ...

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  16. The curve y=ax^2+bx has minimum at (2,-12) on it. Then (a,b) =

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  17. If f(x) = a/x +bx has minimum at (2,1) then (a,b) =

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  18. If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then

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  19. If a quadratic function in x has the value 9 when x=1 and has maximum ...

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  20. A cubic function of x has maximum 10 and minimum -5/2, when x = -3 and...

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