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Examine if Rolle’s theorem is applicable...

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example?`f(x) = [x]` for `x in [-2,2]`

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PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Verify Rolle’s theorem for the function f(x) = x^2 + 2x - 8, x in [-4,...

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  2. Examine if Rolle’s theorem is applicable to any of the following funct...

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  3. Examine if Rolle’s theorem is applicable to any of the following funct...

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  4. Examine if Rolle’s theorem is applicable to any of the following funct...

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  5. If f:[-5,5] rarr R is a differentiable function and if f'(x) does not...

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  6. Verify Mean Value Theorem, if f(x) = x^2-4x-3, in the interval [a, b],...

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  7. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

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  8. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

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  9. Differentiate w.r.t. x the function : (3x^2 - 9x + 5)^9

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  10. Differentiate w.r.t. x the function : sin^3x + cos^6 x

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  11. Differentiate w.r.t. x the function : (5x)^(3cos2x)

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  12. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

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  13. Differentiate w.r.t. x the function : cos^-1(x/2)/sqrt(2x+7), x lies b...

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  14. Differentiate w.r.t. x the function : cot^-1[(sqrt(1+sinx) + sqrt(1-si...

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  15. Differentiate w.r.t. x the function : (logx)^logx, x>1

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  16. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

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  17. Differentiate w.r.t. x the function : (sinx - cosx)^(sinx-cosx), x lie...

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  18. Differentiate w.r.t. x the function : x^x + x^a + a^x + a^a, for some ...

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  19. Differentiate w.r.t. x the function : x^(x^2-3) + (x-3)^(x^2), for x>...

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  20. Find dy/dx if y =12(1-cost), x =10(t-sint)

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