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If f(x) = |{:(sinx,sina, sin b),(cos x ,...

If `f(x) = |{:(sinx,sina, sin b),(cos x , cos a, cos b),(tanx,tana,tanb):}|`,where `0 lt a lt b lt ( pi )/(2)`, then the equation `f'(x) = 0` has, in the interval (a,b)

A

Atleast one root

B

atmost one root

C

no root

D

exactly one root

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The correct Answer is:
A
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AAKASH SERIES-MEAN VALUE THEOREMS-PRACTICE SHEET (EXERCISE-I (LEVEL-I))
  1. If f(x) = |{:(sinx,sina, sin b),(cos x , cos a, cos b),(tanx,tana,tanb...

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  2. The value of 'c' by Rolle's Theorem for which f(x) =1-root(3)(x^(4) i...

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  3. f(x) - log (x^(2) + 2) - log 3 in [-1, 1]

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  4. If 2a+3b+6c=0 , then at least one root of the eqution ax^2+bx+c=0 lies...

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  5. If f(x) = cos x , a = ( - pi )/(2) then the value of 'c' of Rolle's th...

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  6. If f(x) satisfies Rolle's theorem for f(x) in [a,b] then int(a)^(b) f'...

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  7. Rolle's theorem cannot be applicable for

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  8. Value of 'c' of Rolle's theorem for f(x) = |x| in [-1,1] is

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  9. Given n is a positive integer for the function f(x) = 5x(x-2)^(n), x i...

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  10. If (a(0))/(n+1) + ( a(1))/( n ) + ( a(2))/( n -1)+"......"+ (a(n-1))/...

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  11. The value of 'c' in Rolle's theorem for f(x) = log ((x^(2) + ab)/(x(a...

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  12. Rolle's theorem holds for the function x^(3) + bx^(2) + cx, 1 le x le...

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  13. Let f(x) and g(x) be differentiable functions for 0 le x le 1 such t...

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  14. Let f(x) = sqrt(x-1) + sqrt(x+ 24-10sqrt(x-1)),1 lt x lt 26 be real va...

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  15. Rolle's theorem can not applicable for

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  16. If f be a continuous function on [0,1], differentiable in (0,1) such t...

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  17. Let f : [2,7] rarr [ 0 , oo) be a continuous and differentiable funct...

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  18. A value of c for which the conclusion of Mean Value Theorem holds for ...

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  19. The value of 'c' in Lagrange's mean value theorem for f(x) = log x on...

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  20. The value of 'c' in Lagrange's mean value theorem for f(x) = x^(3)-2x^...

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