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If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1),g(0)=0 and f(1) =6 , then for some `c in (0,1)`

A

`f^'( c)=g^'(c )`

B

`f^'(c ) =2g^' (c ) `

C

`2f^'(c ) =g^'(c )`

D

`2f^'( c) -3g^'(c )`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-APPLICATIONS OF DIFFERENTIATION-EXERCISE 1D (MEAN VALUE THEOREMS)
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  2. The constant c of the Lagrange's mean value theorem for the function f...

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  3. The constant c of Lagrange's theorem for f(x)=x^3-4x^2+4x "in" [0,2] i...

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  4. The constant c of Lagrange's theorem for f(x)=x(x-1)(x-2) "in" [0,1//2...

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  5. The constant c of Lagrange's theorem for f(x)=(x-1)(x-2)(x-3) "in" [0...

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  6. The constant c of Lagrange's theorem for f(x) =x/(x-1) "in" [2,4] is

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  7. The constant c of Lagrange's mean value theorem for f(x) =2 sin x+ sin...

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

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

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  10. The constant c of Lagrange's theorem for f(x)=lx^2+mx+n(lne0) in [a,b]...

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  11. The constant c of Lagrange's theorem for f(x)=lx^2+mx+n(lne0) in [a,b]...

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  12. The constant theta of Lagrange's theorem for f(x) =x^2-2x+3 in [1,3/2]...

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  13. Lagrange's theorem can not be applicable for

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  14. Lagrange's theorem can not be applicable for

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  15. If f(x) satisfies Lagrange's mean value theorem in [a,b] then there ex...

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  16. The constant c of Cauchy's mean value theorem for f(x) =x^2,g(x)=x^3 "...

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  17. The constant c of Cauchy's mean value theorem for f(x)=sqrtx,g(x)=1//s...

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  18. The constant c of cauchy's mean value theorem for the functions f(x) =...

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  19. The constant c of Cauchy's mean value theorem for f(x) =e^x,g(x)=e^(-x...

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  20. If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1)...

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