Home
Class 12
MATHS
Let f(x)=a(x-x1)(x-x2)\ w h e r e\ a ...

Let `f(x)=a(x-x_1)(x-x_2)\ w h e r e\ a ,\ x_1a n d\ x_2\ ` are real numbers such that `a\ !=0\ a n d\ x_1+\ x_2=0.` Then which of the following statements is/are always correct? `f(x)` is increasing in `(-oo,0)\ ` and decreasing in `(0,oo)` `f(x)` is decreasing in `(-oo,0)` and increasing in `(0,oo)` `f(x)` is non monotonic on R `f(x)` has an extremum point

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

1.Prove that the function f(x)=log_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if '0

Prove that the function f(x)=(log)_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo). if '0

f(x)=int(2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2))))dx then fis (A) increasing in (0,pi) and decreasing in (-oo,0)(B) increasing in (-oo,0) and decreasing in (0,oo)(C) increasing in (-oo,oo) and (D) decreasing in (-oo,oo)

Prove that the function f(x)=(log)_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if 0

Let f be the function f(x)=cos x-(1-(x^(2))/(2))* Then f(x) is an increasing function in (0,oo)f(x) is a decreasing function in (-oo,oo)f(x) is an increasing function in (-oo,oo)f(x) is a decreasing function in (-oo,0)

Without using the derivative,show that the function f(x)=|x| is strictly increasing in (0,oo) strictly decreasing in (-oo,0)

Show that f(x)=(1)/(x) is a decreasing function on (0,oo)

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,(pi)/(e)), decreasing in ((pi)/(e),oo) decreasing in (0,(pi)/(e)), increasing in ((pi)/(e),oo)

Prove that the function f(x)=log_(e)x is increasing on (0,oo)

Let f''(x)gt0 and phi(x)=f(x)+f(2-x),x in(0,2) be a function then the function phi(x) is (A) increasing in (0,1) and decreasing (1,2) (B) decreasing in (0, 1) and increasing (1,2) (C) increasing in (0, 2) (D) decreasing in (0,2)

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. On which of the following intervals is the function f given by f(x)=x...

    Text Solution

    |

  2. Let f(x)=1+\ x\ ln\ (x+\ sqrt((x^2)+1))-\ sqrt((1)+x^2)a n d\ h(x)=f...

    Text Solution

    |

  3. Let f(x)=a(x-x1)(x-x2)\ w h e r e\ a ,\ x1a n d\ x2\ are real n...

    Text Solution

    |

  4. Let f be a continuous function on R and satisfies f(x)=e^x + int0^1 e^...

    Text Solution

    |

  5. Consider the function f: R->\ R fined as f\ (x)\ =x\ +\ s in\ x . ...

    Text Solution

    |

  6. For the function f(x)\ =\ 1n\ (1-1n\ x) which of the following do ...

    Text Solution

    |

  7. Find the intervals in which f(x)=sinx-cosx , where 0 lt x lt2pi is in...

    Text Solution

    |

  8. Find the greatest & the least values of the following functions in ...

    Text Solution

    |

  9. Find the greatest and the least values of the following functions i...

    Text Solution

    |

  10. If b > a, find the minimum value of |(x-a)^3+|(x-b)^3|, x in R

    Text Solution

    |

  11. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  12. If f(x)=2e^x-ae^(-x)+(2a+1)x-3 monotonically increases for AA x in R,...

    Text Solution

    |

  13. Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)...

    Text Solution

    |

  14. Using L M V T prove that tanx > x in (0,pi/2),

    Text Solution

    |

  15. For what value of adot,\ a n d\ b does the function f(x)={3\ \ ...

    Text Solution

    |

  16. If f is a continuous function on the interval [a,b] and there exists ...

    Text Solution

    |

  17. Prove that following inequalities sinxlt=xlt=tanx\ AA\ in [0,pi/2...

    Text Solution

    |

  18. Find the intervals of monotonicity of the following f(x)=2x^2-"ln"|...

    Text Solution

    |

  19. Let f(x) be a increasing function defined on (0,\ oo)dot If f...

    Text Solution

    |

  20. Prove that f(x)=x/(sinx) is an increasing function while g(x)=x/...

    Text Solution

    |