Home
Class 12
MATHS
Examine the differentiability of f(x) =...

Examine the differentiability of f(x) `= 2x^(2)+ 1 ` at x = 1 .

Text Solution

Verified by Experts

The correct Answer is:
Therefore, f' (1) exists and its value = 4 i.e. f (x) is differenatible at x = 1 .
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Multiple Choice Type Questions|14 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Very short Answer Type Questions|38 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 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 the differentiability of f(x) =2x+|x-1| at x = 1

Examine the continuity and differentiability of f (x) =2x^(2)+1 " at "x=1 .

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 .

Given {:(f(x)=x^(2)-2x+3," ""when "xlt1),(=2," ""when "x=1),(=2x^(2)-5x+5," ""when "x gt1):} Examine the differentiability of the function at x = 1 .

Discuss the differentiability of f(x)=|x[x]| ,-1 < x <= 2

Examine the differentiability of the function f(x)=|cosx| at x=(pi)/(2) .

Discuss the differentiability of f(x)=|x-1|+|x+1|

A function f (x) is defined as follows : f (x) = 3 + 2x , when -(3)/(2)ltx lt0 =3-2x , when 0ltxlt (3)/(2) Examine the differentiability of f (x) at x = 0

A function f (x) is defined as follows : f(x)={{:(5+2x,"when " -(5)/(2)ltxle0),(5-2x,"when "0ltxlt(5)/(2)):} Examine the continuity and differentiability of f (x) at x= 0

Examine the continuity of the function f(x)= 2x^(2)-1" at "x=3 .

CHHAYA PUBLICATION-DIFFERENTIATION-Example
  1. If y = f (x) =x^(2)+2x-3 , find the increment of y corresponding to th...

    Text Solution

    |

  2. If y = f(x) = 5 , show that Delta y = 0 .

    Text Solution

    |

  3. Examine the differentiability of f(x) = 2x^(2)+ 1 at x = 1 .

    Text Solution

    |

  4. Given, f (x) = x when x ge 0 = - x , when x lt 0

    Text Solution

    |

  5. (Find using principle the derivatives of the following functions w.r.t...

    Text Solution

    |

  6. (Find using principle the derivatives of the following furctions w.r.t...

    Text Solution

    |

  7. (Find using principle the derivatives of the following furctions w.r.t...

    Text Solution

    |

  8. (Find using principle the derivatives of the following furctions w.r.t...

    Text Solution

    |

  9. (Find using principle the derivatives of the following furctions w.r.t...

    Text Solution

    |

  10. Find from the definition, the derivatives of e^(4x) at x = 0

    Text Solution

    |

  11. Find from the definition, the derivatives of log 5x at x = 2

    Text Solution

    |

  12. Find from the definition, the derivatives of cosec 3x at x = (pi)/...

    Text Solution

    |

  13. Find from the definition, the derivatives of x^(-3/(2)) at x = 3

    Text Solution

    |

  14. Find from the definition, the derivatives of sqrt(px+q)

    Text Solution

    |

  15. Find from the definition, the derivatives of (px+q)/(ax+b)

    Text Solution

    |

  16. Find from the definition, the derivatives of (1)/(sqrt(ax+b))

    Text Solution

    |

  17. Find from the definition, the derivatives of sqrt(ax^(2)+bx+c)

    Text Solution

    |

  18. Find from the definition, the derivatives of cos^(2)x

    Text Solution

    |

  19. Find from the definition, the derivatives of sin(x^(2))

    Text Solution

    |

  20. Find from the definition, the derivatives of tan^(-1)x

    Text Solution

    |