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if f(x)=(x -4) (x-5) (x-6) (x-7) then, (...

if f(x)=(x -4) (x-5) (x-6) (x-7) then, (A) f'(x) =0 has four roots (B) three roots f'(x) =0 lie in (4,5) `uu(5,6) uu(6,7)` (C) the equation `f'(x) =0` has only one real root. (D) three roots of f'(x) =0 lie in (3,4) `uu (4,5) uu (5,6)`

A

f'(x)=0 has four roots

B

three roots of `f'(x)=0` line in (4,5) `uu (5,6) uu (6,7)`

C

the equation `f'(x)=0` hs only one root

D

three roots of `f'(x)=0` line `in (3,4)uu(4,5)uu(5,6)`

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B
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OBJECTIVE RD SHARMA ENGLISH-MEAN VALUE THEOREMS-Exercise
  1. Let (a0)/(n+1)+(a1)/n+(a2)/(n-1)++(a(n-1))/2+an=0. Show that there e...

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  2. The number of values of k for which the equation x^3-3x+k=0 has two di...

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  3. if f(x)=(x -4) (x-5) (x-6) (x-7) then, (A) f'(x) =0 has four roots (...

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  4. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

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  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

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  6. The equation x log x = 3-x has, in the interval (1,3) :

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  7. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

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  8. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

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  9. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

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  10. The value of c in Lagrange's theorem for the functin f(x)=log sin x in...

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  11. n is a positive integer. If the value of c presecribed in Rolle's th...

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  12. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

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  13. The number of real roots of the equation e^(x-1)+x-2=0 is 1 (b) 2 (...

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  14. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

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  15. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

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  16. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

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  17. If from Largrange's mean value theorem, we have f'(x(1))=(f'(b)-f(a))...

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  18. Rolle's theorem is applicable in case of phi(x) = a^sin x,a>0 in

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  19. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

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  20. When the tangent the curve y=x log (x) is parallel to the chord joinin...

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