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

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

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find 'c' of Lagrange's Mean Value Theorem for the functions: f(x) = ...

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

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

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  4. Verify Lagrange's Mean Value Theorem for the function : f(x) = x (x - ...

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  5. Verify Lagrang'e Mean value Theorem for the function: f(x) = {:{(2+x...

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

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  7. Find a point on the curve y=x^(3), where the tangent to the curve is p...

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  8. Find a point on the curve y = x^3 - 3x, where the tangent is parallel ...

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

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

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  11. Examine the continuity of the function: f(x) = {:((x-4)/(2(x-4)), if...

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  12. Find the value of 'k', such that the function : f(x) = {:{(2x^(x+2)-...

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  13. Given f(x) =1/(x-1). Find the points of discontinuity of the composite...

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  14. Find f' (x) when f(x) = 2^(cos^2x)

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  15. Find f' (x) when f(x) = sin^-1(1/sqrt(x+1))

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  16. If sinx = (2t)/(1+t^2), tan y = (2t)/(1-t^2), find dy/dx

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  17. If y=sec^-1(1/(4x^3 -3x)), find dy/dx

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  18. Find dy/dx when tan^-1(x^2+y^2)=0

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  19. Examine the differentiability of the function f(x) = {:{(x[x], if 0 le...

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  20. Show that |x-5| is continuous but not differentiable at x =5.

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