Home
Class 12
MATHS
Let f(x) be a differentiable even functi...

Let f(x) be a differentiable even function, consider the following statements :
(i) f'(x) is an even function.
(ii) f'(x) is an odd function.
(iii) f'(x) may be even or odd.
Which of the above statements is/are correct ?

A

(i) only

B

(i) and (iii)

C

(ii) only

D

(ii) and (iii)

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 4|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 6|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 2|80 Videos

  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even function.

Statement - I : If f(x) is an odd function, then f'(x) is an even function. Statement - II : If f'(x) is an even function, then f(x) is an odd function.

If f (x) is an even function and f'(0) exists, show that f'(0) = 0 .

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

If f(z) is an odd function, prove that, int_(a)^(x)f(z)dz is an even function.

Let f(x) be a differentiable function and f'(4)=5 . Then lim_(x to 2) (f(4) -f(x^(2)))/(x-2) equals

If f(x) is an odd function then int_(-a)^(a)f(x) is equal to-

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

Prove that f(x)gi v e nb yf(x+y)=f(x)+f(y)AAx in R is an odd function.

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 3
  1. The values of x, at which the first derivative of the function (x+(1)...

    Text Solution

    |

  2. If f(x)=sin3x cos4x, then the value of f''((pi)/(2)) is -

    Text Solution

    |

  3. Let f(x) be a differentiable even function, consider the following sta...

    Text Solution

    |

  4. If y=x+x^(2)+x^(3)+…oo where |x| lt 1, then for |y| lt 1 the value of...

    Text Solution

    |

  5. Find which function does not obey mean value theorem in [0, 1] -

    Text Solution

    |

  6. The derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2)) " at...

    Text Solution

    |

  7. The derivative of the function f(x)=log(5)(log(7)x)[x gt 7] is -

    Text Solution

    |

  8. If 2y=(x-a)sqrt(2ax-x^(2))+a^(2)"sin"^(-1)(x-a)/(a), then the value of...

    Text Solution

    |

  9. The value of lim(x to 0)(1+3x)^((x+2)/(x)) is -

    Text Solution

    |

  10. If y=x^(3) then the value of ((d^(2)y)/(dx^(2)))/([1+((dy)/(dx))^(2)]^...

    Text Solution

    |

  11. If x=(1)/(z), y=f(x) and (d^(2)y)/(dx^(2))=kz^(3)(dy)/(dz)+z^(4)(d^(2...

    Text Solution

    |

  12. If xy=ax^(2)+(b)/(x), then the value of x^(2)(d^(2)y)/(dx^(2))+2x(dy...

    Text Solution

    |

  13. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

    Text Solution

    |

  14. Let f(x)={((sin pix)/(5x),"when "x ne 0),(k,"when "x=0):} If f(x) i...

    Text Solution

    |

  15. If int f(x) dx=f(x), then int {f(x)}^(2)dx is equal to -

    Text Solution

    |

  16. The value of int(sqrt(tanx))/(sinx cosx)dx is equal to -

    Text Solution

    |

  17. The value of int(0)^((pi)/(2))x sin x dx is equal to -

    Text Solution

    |

  18. int(-2)^(2)(|x|+|x-1|)dx is equal to -

    Text Solution

    |

  19. The value of int(0)^((pi)/(2))log(tan x)dx is equal to -

    Text Solution

    |

  20. The value of int(0)^(pi)log sin^(2)x dx is equal to -

    Text Solution

    |