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If the function f(x) and phi (x) are con...

If the function f(x) and `phi (x)` are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of functions `f(x) = e^(x), phi (x) = e^(-x) ` is

A

`(a)/(2)`

B

`(a-b)/(2)`

C

`(a+b)/(2)`

D

`(-a+b)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-MEAN VALUE THEOREMS-PRACTICE SHEET (EXERCISE-I (LEVEL-I))
  1. The value of 'c' prescribed by Lagrange's mean value theorem , when f(...

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  2. The value of C in the lagrange's mean value theroem for f(x) = sqrt( x...

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  3. The value of 'theta' of the Lagrange's mean value theorem for f(x) = x...

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  4. The chord joining the points where x=p and x=q on the curve y =a x^(2)...

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  5. Value of 'c' of Lagrange's mean value theorem for f(x) = 2x - x^(2) i...

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  6. If a lt c lt b , and if 1-k(1) lt ln ((b)/(a)) lt k(2) -1 , then ( ...

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  7. If a(1) lt ( 257)^(1//4) -4 lt b (1), then (a(1) , b(1) ) ( a(1) , b(...

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  8. For the function f(x) = (x-1) ( x-2) ( x-3) in [0,4], value of 'c' in ...

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

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  10. The value of c in Lagrange's Mean Value theorem for the function f(x) ...

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  11. The value of 'c' of Lagrange's mean value theorem for f(x) = x^(3) - 5...

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  12. In the mean value theorem, f(b) - f(a) = (b-a) f(c ) , if a= 4, b = 9 ...

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

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  14. If f(x) = x^(n) for 0 lt a lt b and na^(n-1) le (b^(n) - a^(n))/( b-a...

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  15. Let f(x) and g(x) be differentiable functions in (a,b) continuous in [...

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  16. Lagrange's mean value theorem cannot be applied for

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  17. Let f(x) and g(x) be two differentiable functions in R such that f(2) ...

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  18. If the function f(x) and phi (x) are continuous in [a,b] and different...

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  19. Statement 1 : If 27a+9b+3c+d=0, then the equation f(x) =4ax^(3) + 3b^(...

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  20. Assertion (A) : Suppose f is differentiable on R such that 1le f'(x ) ...

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