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Verify LMVT for the following functions ...

Verify LMVT for the following functions on the intervals shown against them and find the possible values of c :
`f(x)=logx, x in [1, e]`.

Text Solution

Verified by Experts

The correct Answer is:
`c=e-1`.
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-APPLICATIONS OF DERIVATIVES -Examples for Practice
  1. If Rolle's theorem holds for the function f(x)=ax^(3)+bx^(2)+5x+1, x...

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  2. Verify LMVT for the following functions on the intervals shown agains...

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  3. Verify LMVT for the following functions on the intervals shown agains...

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  4. Find c, if LMVT is applicable for f(x)=(x-3)(x-6)(x-9), x in [3, 5].

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  5. Verify Rolle's theorem for each of the following functions : f(x) = ...

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  6. Test whether the following funtions are increasing or decreasing : f...

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  7. Test whether the following funtions are increasing or decreasing : f...

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  8. Find the values of x such that f(x)=x^(3)+12x^(2)+36x+6 is an increasi...

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  9. Find the values of x such that f(x)=2x^(3)-9x^(2)+12x+2 is a decreasin...

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  10. Find the values of x if f(x)=(x)/(x^(2)+1) is an increasing function

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  11. Find the values of x if f(x)=(x)/(x^(2)+1) is a decreasing function.

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  12. Examine the following functions for maxima and minima : f(x)=2x^(3)-...

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  13. Examine the following functions for maxima and minima : f(x)=x^(2)+(...

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  14. Examine the following functions for maxima and minima : f(x)=3x^(3)-...

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  15. Examine the following functions for maxima and minima : f(x)=x^(2)e^...

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  16. Examine the following functions for maxima and minima : Show that f(...

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  17. Examine the following functions for maxima and minima : Find the max...

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  18. Find two positive numbers x and y such that x+y=60 and x y^3 is max...

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  19. Divide the number 84 into two parts such that the product of one part ...

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  20. If x+y=8, then show that the maximum value of x^(2)y is (2048)/(27).

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