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

If `f(x)=x.e^(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

Verified by Experts

The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-APPLICATION OF DERIVATIVES-Assignment SECTION-B( Objective Type Questions ( One option is correct ))
  1. If a function f(x) increases in the interval (a, b). then the function...

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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. If f(x)=x.e^(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 root ...

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

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  7. If f(x)=x/(sinx) \ a n d \ g(x)=x/(tanx),w h e r e \ 0ltxlt=1, then in...

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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-a)^2+(x-b)^2+(x-c)^2dot Then, f(x) has a minimum at x= (a...

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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 extreme values at x=-1 a n d a t x=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. The number which exceeds its square by the greatest possible quanti...

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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 follows: f(x)=sin(x^2-3x),xlt=0; a n...

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  17. If lambda, mu are real numbers such that , x^(3)-lambdax^(2)+mux-6=0 h...

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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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