Home
Class 12
MATHS
For the function f(x)={{:(,|x-3|,x ge 1)...

For the function f(x)=`{{:(,|x-3|,x ge 1),(,(x^(2))/(4)-(3x)/(2)+(13)/(4),x lt 1):}` which one of the folllowing is incorrect

A

not continous at x=1

B

not derivable at x=1

C

continous and derivable at x=1

D

continous at x=1 but not derivable at x=1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|30 Videos

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise HIGHER ORDER DERIVATIVES|32 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

Similar Questions

Explore conceptually related problems

The function f(x)={{:(|x-3|",", x ge1),(((x^(2))/(4))-((3x)/(2))+(13)/(4)",", x lt 1):} is

The function {{:(|x-3|,,ifxge1),((x^(2))/(2)-(3x)/(2)+(13)/(4),, if xlt 1):} is

The function f(x)=[|x-3,x<=1 and ((x^(2))/(4))-((3x)/(2))+((13)/(4)),x<1 is

The function defined by f(x)={|x-3|,x>=1 and (1)/(4)x^(2)-(3)/(3)x+(13)/(4),x<

If |3x-2|+|3x-4|+|3x-6| ge 12, then which of the following is/are incorrect -

Let f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4",", x ge 3):} and g(x)={{:(x-3",", x lt 4),(x^(2)+2x+2",", x le 4):} , which one of the following is/are true?

TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If f(x) = {:{((x -1)/(2x^(2) - 7 x +5) , " for " x ne 1) , (-1/3 ...

    Text Solution

    |

  2. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

    Text Solution

    |

  3. For the function f(x)={{:(,|x-3|,x ge 1),(,(x^(2))/(4)-(3x)/(2)+(13)/(...

    Text Solution

    |

  4. If f(x) = x for x le 0 = 0 for x gt 0, then f(x) at x = 0 is

    Text Solution

    |

  5. At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt o...

    Text Solution

    |

  6. Define f(x) = {{:(x^(2)+bx+c , ",",x lt 1),(x,",",x ge 1):}. If f(x) i...

    Text Solution

    |

  7. If f is differentiable at x=1, Then lim(x to1)(x^2f(1)-f(x))/(x-1) is

    Text Solution

    |

  8. if f(2)=4,f'(2)=1 then lim(x->2){xf(2)-2f(x)}/(x-2)

    Text Solution

    |

  9. If f(x) is differentiable at x=a, then lim(x toa)(x^2f(a)-a^2f(x))/(x-...

    Text Solution

    |

  10. Suppose f(x) is differentiable at x = 1 and lim(h->0) 1/h f(1+h)=5, th...

    Text Solution

    |

  11. Let f : R to R be a function defined by f(x) = max. {x, x^(3)}. The s...

    Text Solution

    |

  12. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  13. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

    Text Solution

    |

  14. If the function g(x) = {(ksqrt(x+1) " when " 0 le x le 3),(mx + 2 " ...

    Text Solution

    |

  15. Let S={t in R: f(x)=|x-pi|(e^(|x|)-1)sin|x| is not differentiable at t...

    Text Solution

    |

  16. If y=cos (2x +45^(@) ),then (dy)/(dx) =

    Text Solution

    |

  17. If y=sqrtsinsqrtx, then (dy)/(dx) =

    Text Solution

    |

  18. d/(dx)log|x|e=

    Text Solution

    |

  19. The differential coefficient of f(loge x) w.r.t. x, where f(x) = loge...

    Text Solution

    |

  20. If y=log2 (log2 x), then (dy)/(dx)=

    Text Solution

    |