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f(x) =xe^(x(1-x)), then f(x) is...

`f(x) =xe^(x(1-x)), then f(x) is `

A

Increasing on R

B

Increasing on `[-(1)/(2),1]`

C

Decreasing on R

D

Decreasing non `[-(1)/(2),1]`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE-APPLICATION OF DERIVATIVES-Assignment SECTION-B( Objective Type Questions ( One option is correct ))
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  2. The function f, defined by f(x)=(x^(2))/(2) +In x - 2 cos x increas...

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  3. f(x) =xe^(x(1-x)), then f(x) is

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  4. Which of the following is correct ?

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  5. Find the value of a , if the equation x-sinx=a has a unique r...

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  6. Number of real roots of the equation e^(x-1)-x=0 is

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  7. f(x)=(x)/(sinx ) and g(x)=(x)/(tanx) , where 0 lt x le 1 then in the...

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  8. If f(x)=(p^2-1)/(p^2+1) x^3-3x + log 2 is a decreasing function of x.i...

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  9. Let f(x) = (x-p)^2+ (x -q)^2 + (x - r)^2. Then f(x) has a minimum at ...

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  10. The maximum value of ((1)/(x))^(2x^(2)) is

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  11. If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then ...

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  12. If x in [-1,1] then the minimum value of f(x)=x^(2)+x+1 is

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  13. If ax+(b)/(x) ge c, AA a gt 0 and a,b,c are positive constant then

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  14. Let x be a number which exceeds its square by the greatest possible qu...

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  15. The point (0,3) is nearest to the curve x^(2)=2y at

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  16. Let f(x) be a function defined as below : f(x)=sin(x^(2)-3x) ,x le...

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  17. If lambda, mu be real numbers such that x^3-lambda x^2 + mux-6=0 has i...

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  18. The value of c in Lagrange's mean value theorem for the function f(x) ...

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  19. If a, b, c, d are real numbers such that (3a + 2b)/(c+d)+3/2=0 the...

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  20. If the least area of triangle formed by tangent,normal at any point P ...

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