Home
Class 12
MATHS
If y=f(x) is an odd differentiable funct...

If `y=f(x)` is an odd differentiable function defined on `(-oo,oo)` such that `f^(prime)(3)=-2,t h e n|f^(prime)(-3)|` equals_________.

Text Solution

Verified by Experts

Since f(x) is odd, f(-x)=-f(x) or f'(-x)(-1)=-f'(x)
`"or "f'(-x)=f'(x)`
`therefore" "f'(-3)=f'(3)=-2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise JEE Previous Year|15 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answers Type|3 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f(-pi)=1. The value of |g^n (-pi)| equals __________

Let f(x) be a non-constant twice differentiable function defined on (-oo,oo) such that f(x)=f(1-x)a n df^(prime)(1/4)=0. Then (a) f^(prime)(x) vanishes at least twice on [0,1] (b) f^(prime)(1/2)=0 (c) int_(-1/2)^(1/2)f(x+1/2)sinxdx=0 (d) int_(-1/2)^(1/2)f(t)e^(sinpit)dt=int_(1/2)^1f(1-t)e^(sinpit)dt

Let f(x0 be a non-constant thrice differentiable function defined on (-oo,oo) such that f(x)=f(6-x)a n df^(prime)(0)=0=f^(prime)(x)^2=f(5)dot If n is the minimum number of roots of (f^(prime)(x)^2+f^(prime)(x)f^(x)=0 in the interval [0,6], then the value of n/2 is___

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(7)=3, then the value of f^(prime)(3) is__________

If f(x)=(f(x))/y+(f(y))/x holds for all real x and y greater than 0a n df(x) is a differentiable function for all x >0 such that f(e)=1/e ,t h e nfin df(x)dot

Let f(x y)=f(x)f(y)AAx , y in Ra n df is differentiable at x=1 such that f^(prime)(1)=1. Also, f(1)!=0,f(2)=3. Then find f^(prime)(2)dot

Suppose the function f(x) satisfies the relation f(x+y^3)=f(x)+f(y^3)dotAAx ,y in R and is differentiable for all xdot Statement 1: If f^(prime)(2)=a ,t h e nf^(prime)(-2)=a Statement 2: f(x) is an odd function.

Suppose f is a real-valued differentiable function defined on [1,oo] with f(1)=1. Moreover, suppose that f satisfies f^(prime)(x)=1/(x^2+f^2(x))S howt h a tf(x)<1+pi/4AAxgeq1.

A function f satisfies the condition f(x)=f^(prime)(x)+f^(primeprime)(x)+f^(primeprimeprime)(x) ...... ,where f(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0)=1,t h e nf(x) is (A) e^(x/2) (B) e^x (C) e^(2x) (D) e^(4x)

CENGAGE-DIFFERENTIATION-Exercise (Numerical)
  1. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

    Text Solution

    |

  2. f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(p...

    Text Solution

    |

  3. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

    Text Solution

    |

  4. If x^3+3x^2-9x=c is of the form (x-alpha)^2(x-beta) , then c is equal ...

    Text Solution

    |

  5. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

    Text Solution

    |

  6. Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value ...

    Text Solution

    |

  7. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

    Text Solution

    |

  8. If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f...

    Text Solution

    |

  9. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  10. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

    Text Solution

    |

  11. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |

  12. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

    Text Solution

    |

  13. A nonzero polynomial with real coefficient has the property that f(x)=...

    Text Solution

    |

  14. A function is reprersented parametrically by the equations x=(1+t)/(t^...

    Text Solution

    |

  15. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

    Text Solution

    |

  16. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

    Text Solution

    |

  17. Let f(x)=x+1/(2x+1/(2x+1/(2x+oo))) Compute the value of f(50)dotf^(p...

    Text Solution

    |

  18. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

    Text Solution

    |

  19. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

    Text Solution

    |

  20. Let y be an implicit function of x defined by x^(2x)-2x^(x) cot y-1=0...

    Text Solution

    |