Home
Class 12
MATHS
Let f: \mathbb{R} rarr \mathbb{R} be a t...

Let `f: \mathbb{R} rarr \mathbb{R}` be a twice differentiable function such that `f(x+pi)=f(x)` and `f''(x) + f(x) geq 0` for all `x in \mathbb{R}`. Show that `f(x) geq 0` for all `x in \mathbb{R}`.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)) , then h'(1) is equal to

If f is a real- valued differentiable function such that f(x)f'(x) lt 0 for all real x, then

If f is a real-valued differentiable function such that f(x) f'(x)lt0 for all real x, then

If f is a real-valued differentiable function such that f(x)f'(x)lt0 for all real x, then -

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1) =1 , then

Let f:R to R be such that f(0)=0 and |f'(x)| le 5 for all x. Then f(1) is in

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f'(x)gt0 and g'(x)lt0 for all x in R, then

f(x) is real valued function such that 2f(x) + 3f(-x) = 15 - 4x for all x in R . Then f(2) =

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(3) is

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)...

    Text Solution

    |

  2. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then (a)k<3...

    Text Solution

    |

  3. Let f: \mathbb{R} rarr \mathbb{R} be a twice differentiable function s...

    Text Solution

    |

  4. Show that 5xlt=8sinx-sin2xlt=6x for 0lt=xlt=pi/3dot

    Text Solution

    |

  5. Discuss the number of roots of the equation e(k-xlogx)=1 for different...

    Text Solution

    |

  6. Prove that sin1>cos(sin1)dot Also, show that the equation sin("cos"(si...

    Text Solution

    |

  7. Pa n dQ are two points on a circle of centre C and radius alpha . The ...

    Text Solution

    |

  8. If f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)+(lambda^2-5...

    Text Solution

    |

  9. Let f(x)={(2-|x^2+5x+6|,x!=-2),(a^2+1,x=-2):} then value of 'a' so tha...

    Text Solution

    |

  10. If A >0,B >0 and A+B=pi/3, the maximum value of tanAtanB is

    Text Solution

    |

  11. f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasi...

    Text Solution

    |

  12. If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a...

    Text Solution

    |

  13. The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot The...

    Text Solution

    |

  14. Iff(x)={sin^(-1)(sinx),x >0, pi/2,x=0,tcos^(-1)(cosx),x<0

    Text Solution

    |

  15. f: R to R ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot ...

    Text Solution

    |

  16. Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^...

    Text Solution

    |

  17. If f: RtoRa n dg: RtoR are two functions such that f(x)+f^(primeprime)...

    Text Solution

    |

  18. Let h(x)=x^(m/n) for x in R , where m and n are odd numbers where 0<...

    Text Solution

    |

  19. Find the number of points of maxima and minima of the function. f(x)=1...

    Text Solution

    |

  20. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

    Text Solution

    |