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For what choice of a and b is the functi...

For what choice of `a` and `b` is the function `f(x)={x^2\ \ \ ,\ \ \ xlt=c \ \ \ \ \ \a x+b\ \ \ ,\ \ \ x > c` is differentiable at `x=c` .

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Discuss the differentiability of f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a ...

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  2. If f(x) is differentiable at x=a , find (lim)(x->a)(x^2f(a)-a^2\ f(x))...

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  3. For what choice of a and b is the function f(x)={x^2\ \ \ ,\ \ \ xlt=c...

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  4. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

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  5. A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all ...

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  6. Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

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  7. Show that f(x)=x^(1//3) is not differentiable at x=0 .

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  8. Show that f(x)={12 x-13 ,\ \ \ if\ xlt=3 \ \ \ \ \ 2x^2+5,\ \ \ \ \ i...

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  9. Show that the function f defined as follows f(x)={3x-2, 0 < x <=1 , 2x...

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  10. Discuss the continuity and differentiability of the function f(x)=|...

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  11. Find whether the following function is differentiable at x = 1 and x...

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  12. Show that the function f(x)={x^msin(1/x), x=0 ,0 ,\ \ \ x!=0 ,\ \ \ \...

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  13. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 , 0\ \ x=0 is d...

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  14. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \...

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  15. Find the values of a and b so that the function f(x)={x^2+3x+a ,\ \ if...

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  16. Show that the function f(x)={|2x-3|\ [x],\ \ xgeq1; \ \ \ \ \ \ \ \ ...

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  17. If f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ ...

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  18. Find the values of a and b , if the function f(x) defined by f(x)={x^2...

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  19. If f(x)=x^2+2x+7 , find f\ '\ (3) .

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  20. Find f\ '\ (2) and f\ '\ (5) when f(x)=x^2+7x+4 .

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