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If f'(x) exists and if f'(x) lt 0 every...

If f'(x) exists and if `f'(x) lt 0` everywhere in the interval ` a le x le b`, then show that f(x) is a decreasing function in `a le x lt b`.

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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3B (Very Short Answer Type Questions)
  1. Verify the truth of Rolle's theorem for the functions: f(x)=sinx-si...

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  2. Show that Rolle's theorem is not applicable to the following functions...

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  3. Show that Rolle's theorem is not applicable to the following functions...

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  4. Show that Rolle's theorem is not applicable to the following functions...

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  5. Show that Rolle's theorem is not applicable to the following functions...

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  6. Show that Rolle's theorem is not applicable to the following functions...

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  7. Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt ...

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  8. Lagrange's mean value theorem is , f(b)-f(a)=(b-a)f'(c ), a lt c lt ...

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  9. Is Lagrange's mean value theorem applicable to the function f(x)=4(6-x...

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  10. If f'(x) exists and if f'(x) lt 0 everywhere in the interval a le x...

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  11. Form Lagrange's mean value theorem formula for the function f(x)=sinx...

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  12. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  13. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  14. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  15. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  16. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  17. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  18. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  19. Verify the truth of Lagrange's mean value theorem formula for the foll...

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  20. If f'(x)=0 for all values of x in an interval, then show that f(x) is ...

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