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Verify Mean Value Theorem, if f(x)=x^3-5...

Verify Mean Value Theorem, if `f(x)=x^3-5x^2-3x`in the interval [a, b], where `a = 1 a n d b = 3`. Find all `c in (1, 3)`for which `f^(prime)(c)=0`.

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The correct Answer is:
Applicable; `c=7/3`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(m) (LONG ANSWER TYPE QUESTIONS (I))
  1. Verify Lagrange's Mean Value Theorem for the functions : f(x)=x^(1//...

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  2. Verify Lagrange's Mean Value Theorem for the functions : f(x)=(x-1)^...

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  3. Verify Lagrange's Mean Value Theorem for the functions : f(x)=1/x in...

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  4. f(x) = 1/(4x-1) in [1,4]

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  5. Verify Lagrange's Mean Value Theorem for the functions : f(x) = |x| ...

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  6. Verify Lagrange's Mean Value Theorem for the functions : f(x)=sqrt(x...

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  7. Verify Lagrange's Mean Value Theorem for the functions : f(x)=sqrt(2...

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  8. Verify Lagrange's Mean Value Theorem for the functions : f(x)=log(e)...

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  9. Verify Lagrange's Mean Value Theorem for the functions : f(x)=x" on ...

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  10. Find 'c' of Lagrange's Mean Value Theorem for the functions : f(x)=...

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  11. Find 'c' of Lagrange's Mean Value Theorem for the functions : f(x)=...

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  12. Find 'c' of Lagrange's Mean Value Theorem for the functions : f(x)=...

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  13. Verify Mean Value Theorem, if f(x)=x^3-5x^2-3xin the interval [a, b],...

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  14. If mean value theorem holds for the function f(x)=(x-1)(x-2)(x-3), x i...

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  15. Verify Lagrange's Mean Value Theorem for the function : f(x)={{:(2+x...

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  16. Find a point on the parabola y=(x-2)^(2), where the tangent is paralle...

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  17. Find a point on the graph of y=x^(3), where the tangent is parallel to...

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  18. Find a point on the curve y=x^3-3x where the tangent is parallel to th...

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  19. Find the co-ordinates of the point at which the tangent to the curve g...

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  20. Use Lagrange's Mean value Theorem to determine a point P on the curve ...

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