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The function in which Rolle's theorem is...

The function in which Rolle's theorem is verified is:

A

`f(x) = log ((x^(2)+ ab)/(a+b))x` (where 0 lt a lt b)

B

f(x) is continuous on [-1, 3]

C

`f(X) - 2+(x-1)^2/3 in [0,2]`

D

`f(x) = cos 1/x in [-1, 1]`

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The correct Answer is:
A
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FIITJEE-APPLICATION OF DERIVATIVE-Assignment Objective (level-1)
  1. If the curves x^(2)/a^(2)+ y^(2)/4 = 1 and y^(3) = 16x intersect at r...

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  2. If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt...

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  3. The function in which Rolle's theorem is verified is:

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  4. f(x)={:{(max g(t), 0let le x , 0le x lepi/2),(min g(t) , xlet lt 0, -p...

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  5. If f''(x)+f'(x)+f^(2)(x)=x^(2) be the differentiable equation of a cur...

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  6. The maximum value of the function f(x)=((1+x)^(0. 6))/(1+x^(0. 6)) in ...

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  7. A is a set containing n(1) elements and B is another set containing n(...

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  8. Let A be the point where the curve 5 alpha ^(2) x ^(3) +10 alpha x ^(2...

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  9. For the curve x^(2)y^(3) = c (where c is a constant), the portion of t...

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  10. Which of the following statements is not true about f(x) = 1+x+ x^(2)/...

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  11. The set of all values a for which f(x) = (a^(2) - 3a+2)(cosx/2)+(a-1)x...

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  12. If f: RvecRa n dg: RvecR are two functions such that f(x)+f^(x)=-xg(x)...

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  13. The largest possible value of the expression f(n) = sinx(1) cosx(2) + ...

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  14. A function g(theta ) = int(0)^(sin^(2)theta) f(x)dx + int(0)^(cos^(2...

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  15. The functio f(x)=tanx+(1)/(x), AA x in (0, (pi)/(2)) has

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  16. The function f(x) = min {|x|, sqrt(1-x^(2))}, -1lt x lt 1 possesses

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  17. If a, b, c, d, e and f are non negative real numbers such that a +b+...

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  18. For the function f(x) = cos^(-1)x + cos ^(-1) x^(2) which of the follo...

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  19. The greatest value of ax + by, when x and y are positive and x^(2)+ y ...

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  20. If x + y=4 and x >=0, y>= 0 find the maximum value of x^3y.

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