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Find “theta ” of the Rolle’s theorem for...

Find “`theta` ” of the Rolle’s theorem for the function `f(x ) = x^(2) -5x + 7` in [2,3],
at least one root
atmost one root

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AAKASH SERIES-MEAN VALUE THEOREMS-EXERCISE
  1. Find “theta ” of the Rolle’s theorem for the function f(x ) = x^(2) -5...

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  2. f(x) = x^(2) - 1 in [-1,1]

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  3. f(x) = x^(2) -5x + 6 in [-3, 8]

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  4. f(x) = x^(2) + 4 in [-3, 3]

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  5. f(x) = (x^(2) - 1 ) (x - 2) in [-1, 2]

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

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  7. The constant c of Rolle's theorem for the function f(x)=2x^3+x^2-4x-2 ...

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  8. Find c of the R olle’s theorem for the functions f(x)=log(x^(2)+3)/(4x...

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  9. The value of 'c' in Lagrange's mean value theorem for f(x) = ( x - a)m...

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  10. If f(x) = x^(3) + bx^(2) + ax satisfies the conditions of Rolle's the...

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  11. If a + b + c = 0, then the equation 3ax^(2) + 2bx + c = 0 has, in the ...

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  12. If 27a+9b+3c+d=0, then the equation 4ax^(3)+3bx^(2)+2cx+d =0 has atlea...

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  13. Rolle's theorem cannot be applicable for

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  14. The value of 'c' in Lagrange's thorem for f(x) = lx^(2) + mx + n [l ne...

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  15. If f'(x) = (1)/(1+x^(2)) for all x and f(0) = 0, then:

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  16. Let f be a function which is continuous and differentiable for all rea...

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  17. In [0,1], Lagrange's mean value theorem is not applicable to (a) f(...

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

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  19. The value of 'a' for which x^(3) -3x +a=0 has two distinct roots in [...

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  20. Let R rarr R be a continuous function define by f(x ) =(1)/(e^(x)+2e) ...

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  21. The real number k for which the equation, 2x^(3)+3x+k=0 has two distin...

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