Home
Class 12
MATHS
Let f(x) = {:{(|x| for 0<|x|le1), (1 for...

Let `f(x) = {:{(|x| for 0<|x|le1), (1 for x = 0):}` then

A

f has a local minimum at 0

B

f has a local maximum at 0

C

f has a point of inflextion at 0

D

none of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    PRADEEP PUBLICATION|Exercise EXERCISE|502 Videos

  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = (x+|x|)/x for x ne 0 and let f (0) = 0, Is f continuous at 0?

Let f(x) = {:{(4x-3, if x<0),(4x + 3, if x ge 0):} . Is it a continuous function? Justify your answer.

Let f(x) = x|x| for all x in R . Discuss continuity and derivability of f(X) at x = 0

Let f(x) = |{:(cos x ,1,0 ),(1,2cosx,1),(0,1,2cosx):}| then

Let f(x)= {(|x|+1,",", x 0.):} For what value(s) of ‘a’ does lim_(x rarr a) f(x) exist ?

Let f (x) { {:(1+x"," , 0 le x le 2),( 3-x"," ,2 lt x le 3):}: Find fof.

Let f(x) = |x| cos (1/x) for x ne 0 . Write the down the value of (f) (0) if f is continuous at x = 0

Let f(x) and g(x) be functions which take integers as arguments. Let f(x + y) =f(x)+ g(y) + 8 for all intege x and y. Let f(x) = x for all negative integers x and let g (8) = 17 . Find f(0).

Let f(x) = {:{((sinx)/x + cosx, when x ne 0),(2, when x = 0):} show that f (x) is continouous at x = 0.

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. The point on the curv3e y = sqrt(4x-3)-1, at which the slope of the ta...

    Text Solution

    |

  2. The point on the curve y = x^2 - 4 x + 4 at which the tangent is paral...

    Text Solution

    |

  3. The tangent to the curve given by: x=e^t cos t,y =e^t sin t at t = pi/...

    Text Solution

    |

  4. The tangent to the curve y=e^(2x) at the point (0, 1) meets x-axis at ...

    Text Solution

    |

  5. The points at which the tangents to the curve y=x^(3)-12x+18 are paral...

    Text Solution

    |

  6. The point at which the curves x^2 =y and y^2 = x cut orthogonally is

    Text Solution

    |

  7. The equation of tangent to the curve y(1+x^(2))=2-x, where it crosses ...

    Text Solution

    |

  8. If the curve at ay+x^(2)=7 and x^(3)=y, cut orthogonally at (1, 1), th...

    Text Solution

    |

  9. The function f(x) = x has

    Text Solution

    |

  10. The function f(x) = 2x^3 - 6x^2 + 6x + 5 has

    Text Solution

    |

  11. Let f(x) = {:{(|x| for 0<|x|le1), (1 for x = 0):} then

    Text Solution

    |

  12. The abscissa of the point on the curve 3y=6x-5x^3, the normal at which...

    Text Solution

    |

  13. At x = 5pi/6, f(x) = 2 sin 3x + 3 cos 3 x is

    Text Solution

    |

  14. The two curves x^3 - 3x y^2 + 2 = 0 and 3x^2y - y^3 - 2 = 0 intersect ...

    Text Solution

    |

  15. The function f(x) = loge(x^3 + sqrt(x^6 +1)) is

    Text Solution

    |

  16. Let f(X) = tan^-1 g(x), where g (x) is monotonically increasing for 0<...

    Text Solution

    |

  17. Function f(X) = cos x - 2 lambdax is monotonic decreasing when

    Text Solution

    |

  18. Let g(x)=2f(x/2)+f(2-x) and f''(x) < 0 AA x in (0,2). If g(x) increa...

    Text Solution

    |

  19. f(x) = logAx is increasing on R, if

    Text Solution

    |

  20. The function f(x) = a^x is strict decreasing on R, If

    Text Solution

    |