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A function f (x) is defined as follows :...

A function f (x) is defined as follows :
`f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):}`
Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

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The correct Answer is:
not differntiable , discontinuous
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CHHAYA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -EXERCISE 2A ( Long Answer Type Questions)
  1. If the following function f (x) is continuous at x = 0 , find k : ...

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  2. The function f(x)=(x^(3)-1)/(x-1) is undefined at x = 1 . Redefine the...

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  3. Show that the function f(x)={{:(x+(x+2)/(|x+2|),"when " xne-2),(" "-...

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  4. If the function f(x)={{:(3ax+b,"for "xgt1),(" " 11,"when " x=1),(5...

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  5. Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi...

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  6. Let f(x)={{:((sin(a+1)x+sinx)/(x)",","when " xlt0),(" c,","wh...

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  7. Show that the function f(x)=|sinx+cosx| is continuous at x = pi.

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  8. Show that the function g(x)=x-[x] is discontinuous at all integral po...

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  9. Find from the first principle , the derivatives of the following funct...

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  10. Find from the first principle , the derivatives of the following funct...

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  11. Find from the first principle , the derivatives of the following funct...

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  12. Find from the first principle , the derivatives of the following funct...

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  13. Find from the first principle , the derivatives of the following funct...

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  14. Find from the first principle , the derivatives of the following funct...

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  15. Find from the first principle , the derivatives of the following funct...

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  16. f(x)={{:(x^(2)-2x+3,"for "xlt1),(" "2,"for "x=1),(2x^(2)-5x+5,"for ...

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  17. A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt...

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  18. If the function f (x) defined below is differentiable at x = 1 then fi...

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  19. If the function f(x)={{:(2x+3",","when "xle1),(ax^(2)+bx",","when ...

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  20. If f (x) is an even function and f'(0) exists, show that f'(0) = 0 ...

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