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Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.

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We know that the modulus function,
`f(x)=∣x∣` is continuous but not differentiable at `x=0`.
So, `f(x)=∣x∣+∣x−1∣+∣x−2∣+∣x−3∣+∣x−4∣` is continuous ,
but not differentiable at `x=0,1,2,3,4`
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Find the derivative of the function f defined by f(x)=m x+c at x=0 ...

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  2. Examine the differentiability of the function f defined by f(x)={2x...

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  3. Write an example of a function which is everywhere continuous but f...

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  4. Discuss the continuity and differentiability of f(x)=|log|x|| .

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  5. Discuss the continuity and differentiability of f(x)=e^(|x|) .

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  6. Discuss the continuity and differentiability of f(x)={(x-c)cos(1/(x...

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  7. Is |sinx| differentiable? What about cos|x| ?

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  8. Define differentiability of a function at a point.

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  9. Is every differentiable function continuous?

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  10. Is every continuous function differentiable?

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  11. Give an example of a function which is continuous but not different...

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  12. If f(x) is differentiable at x=c , then write the value of (lim)(x-...

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  13. If f(x)=|x-2| write whether f\ '\ (2) exists or not.

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  14. Write the points where f\ (x)=|(log)e x| is not differentiable.

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  15. Write the points of non-differentiability of f(x)=|log|x|| .

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  16. Write the derivative of f\ (x)=|x|^3 at x=0 .

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  17. Write the number of points where f(x)=|x|+|x-1| is continuous but n...

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  18. If (lim)(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of...

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  19. Write the value of the derivative of f(x)=|x-1|+|x-3| at x=2 .

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  20. If f(x)=sqrt(x^2+9) , write the value of (lim)(x->4)(f(x)-f(4))/(x-4) ...

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