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If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexl...

If `f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):}`, then f(x) is

A

both f'(1) and f'(2) do not exist

B

f'(1) exists but f'(2) does not exist

C

f'(2) exists but f'(1) does not exist

D

both f' (1) and f'(2) exists

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The correct Answer is:
A
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Newton-Leinbnitz's formula states that d/dx(int(phi(x))^(psi(x)) f(t)d...

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  2. f(x) is not differentiable at x=c if either Lf'( c )neRf'( c ) [if the...

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  3. If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):}, then f(x) is

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  4. f(x) is not differentiable at x=c if either Lf'( c )neRf'( c ) [if the...

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  5. Let f(x) be a polynomial satisfying f(0)=2, f'(0)=3 and f''(x)=f(x). A...

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  6. Match List - I with List-II

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  7. If [x] denotes greatest integer le x, then match the following limits ...

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  8. Match List - I with List-II

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  9. The value of lim(xrarr1)(x+x^2+x^3+...+x^97-97)/((x-1)) must be M. The...

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  10. If lim(xrarr0)1/x^2(e^(ax)-e^x-x)=3/2, then the value of |alpha|must b...

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  11. If f(x)={(((1-sin^3x))/(3cos^2x), x lt pi/2), (a, x=pi/2), ((b(1-sinx)...

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  12. Given, f(x)={((x^4-256)/(x-4), x ne 4), ( lambda, x = 4):}. If f is co...

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  13. If f(x)={((8^x-4^x-2^x+1^x)/x^2, x gt 0),(e^x sinx + pi x + lambda In4...

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  14. If f(x)={(((exp{(x+3)ln27})^(1/27[x])-9)/(3^x-27), x lt 3), (lamda.((1...

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  15. If f(x)={(5+x^2, x lt 1), (x-4, x ge 1):} is jump discontinuous, then ...

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  16. A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for...

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  17. If f(x) is continuous and f(9/2) = 2/9, then find lim(xrarr0)9f((1-cos...

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  18. If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then fi...

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  19. Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), the...

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  20. Number of point of discontinuity of f(x)=tan^2x-sec^2x in (0, 2pi) is

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