Home
Class 12
MATHS
Examine whether f (x) = |x| has a deri...

Examine whether `f (x) = |x| ` has a derivative at x = 0 .

Text Solution

Verified by Experts

The correct Answer is:
`f'(0)` does not exist
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Short AnswerType Questions|63 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|23 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Multiple Choice Type Questions|14 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Examine whether f (x)=|2x| has a derivative at x = 0

Examine whether f(x)=|x+1| has a derivative at x = - 1 .

Given, f'(c) =lim_(xtoc) (f(x)-f(c))/(x-c) , when the limit exists,. Using this difinition investigate whether f(x) =(1)/(x) has a derivative at x = 2 and obtain the derivative, if it exists.

Find the derivative of f(x) = 10x.

Find the derivative of f(x) = x^(2) .

Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and derivative 7 at x=2 . The derivative of the function f(x)-f(4x) at x=1 has the value equal to (a) 19 (b) 9 (c) 17 (d) 14

If f(x)={{:(x+sinx,"when "xlt0),(0,"when "xge0):} examine whether f(x) is continuous at x = 0.

A function f(x) is defined as follows : f(x)=-x," when "x lt0 =2," when "0 lex lt2 =4-x," when "x ge2 Draw the graph of the function and from the graph examine whether f(x) is continuous at x = 0 and x = 2 or not.

A function f(x) is defined as follows : " "f(x)={:{(x-1",","when "x gt 0),(-(1)/(2)",","when "x = 0),( x+1",","when "xlt0):} Draw the graph of the function f(x). From the graph find the value of f(x) at x=-(1)/(2) and examine whether f(x) is continuous at x = 0.

Sketch the graph of f(x)=|x-4|-2. From the graph examine whether f(x) is continuous at x = 4 or not.

CHHAYA PUBLICATION-DIFFERENTIATION-Very short Answer Type Questions
  1. Define the derivative of a function f(x) at an arbitrary point x in it...

    Text Solution

    |

  2. Examine whether f (x) = |x| has a derivative at x = 0 .

    Text Solution

    |

  3. If y = (1)/(x) find (dy)/(dx), also find the value of x for whic...

    Text Solution

    |

  4. If u and v are two differentiable functions of x and y = uv , prove th...

    Text Solution

    |

  5. Given, f'(c) =lim(xtoc) (f(x)-f(c))/(x-c) , when the limit exists,. U...

    Text Solution

    |

  6. Differentiate the following functions w.r.t. x : x^(16)

    Text Solution

    |

  7. Differentiate the following functions w.r.t. x : 3x^(7)

    Text Solution

    |

  8. Differentiate the following functions w.r.t.x : x^(-3)+20sqrt(x)

    Text Solution

    |

  9. Differentiate the following functions w.r.t.x : (2x^(2)+3)/(sqrt(x)...

    Text Solution

    |

  10. Differentiate the followingg functions w.r.t.x : 2x^(4)-(6)/(x^(2)...

    Text Solution

    |

  11. Differentiate the following functions w.r.t.x : (1)/(sqrt(5x))+sqrt...

    Text Solution

    |

  12. Differentiate the following functions w.r.t.x : (x^(2)-2)^(2)

    Text Solution

    |

  13. Differentiate the following functions w.r.t.x : (2x^(2)+3x-4)/(sqrt...

    Text Solution

    |

  14. Differentiate the following functions w.r.t.x : (x^(2)-2x)(x-1)

    Text Solution

    |

  15. Differentiate the following functions w.r.t.x : (x^(4)-3x^(2)-4)/(...

    Text Solution

    |

  16. Differentiate the following functions w.r.t.x : 2+(3)/(x)+(4)/(...

    Text Solution

    |

  17. Differentiate the following functions w.r.t.x : xsqrt(x)-6(x^(2))/...

    Text Solution

    |

  18. Find (dy)/(dx) : y=3log x - 4sqrt(x)+2e^(x)

    Text Solution

    |

  19. Find (dy)/(dx) : y = log (2)x

    Text Solution

    |

  20. Find (dy)/(dx) : y = 2x^(m)-3m^(x)+4e^(x)

    Text Solution

    |