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Verify Rolles theorem for function f(...

Verify Rolles theorem for function `f(x)=(x-1)(x-2)^2` on `[1,\ 2]`

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Given, `f(x)=(x-1)(x-2)^2` is a polynomial function which is continuous and differentiable everywhere and in `[1,2]`

`f(1)=(1-1)(1-2)^2=0`

`f(2)=(2-1)(2-2)^2=0`

`f(1)=f(2)=0`

All condition of Rolle's theorem is satisfied and so there exist `c in (1,2)` such that `f'(c)=0`

`f(x)=(x-1)(x-2)^2`

`f'(x)=(x-2)^2+2(x-1)(x-2)`

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RD SHARMA-MEAN VALUE THEOREMS-Solved Examples And Exercises
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  2. Verify Rolles theorem for function f(x)=x^2-4x+3 on [1,\ 3]

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  3. Verify Rolles theorem for function f(x)=(x-1)(x-2)^2 on [1,\ 2]

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  4. Verify Rolles theorem for function f(x)=x(x-1)^2 on [0,\ 1]

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  5. Verify Rolles theorem for function f(x)=(x^2-1)(x-2) on [-1,\ 2]

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  6. Verify Rolles theorem for function f(x)=x(x-4)^2 on [0,\ 4]

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  7. Verify Rolles theorem for function f(x)=x(x-2)^2 on [0,\ 2]

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  8. Verify Rolles theorem for function f(x)=x^2+5x+6 on [-3,\ -2]

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  9. Verify Rolles theorem for function f(x)=cos2(x-pi//4) on [0,\ pi//2...

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  10. Verify Rolles theorem for function f(x)=sin2x on [0,\ pi//2]

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  11. Verify Rolles theorem for function f(x)=cos2x on [-pi//4,\ pi//4]

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  12. Verify Rolles theorem for function f(x)=e^xsinx on [0,\ pi]

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  13. Verify Rolles theorem for function f(x)=e^xcosx on [-pi//2,\ pi//2]

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  14. Verify Rolles theorem for function f(x)=cos2x on [0,\ pi]

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  15. Verify Rolles theorem for function f(x)=(sinx)/(e^x) on 0lt=xlt=pi

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  16. Verify Rolles theorem for function f(x)=sin3x on [0,\ pi]

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  17. Verify Rolles theorem for function f(x)=e^(1-x^2) on [-1,\ 1]

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  18. Verify Rolles theorem for function f(x)=log(x^2+2)-log3 on [-1,\ 1]

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  19. Verify Rolles theorem for function f(x)=sinx+cosx on [0,\ pi//2]

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  20. Verify Rolles theorem for function f(x)=2sinx+sin2x on [0,\ pi]

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