Home
Class 12
MATHS
A function f(x) having the following pr...

A function f(x) having the following properties,
(i) f(x) is continuous except at x=3
(ii) f(x) is differentiable except at x=-2 and x=3
(iii) `f(0) =0 lim_(x to 3) f(x) to - oo lim_(x to oo) f(x) =3 , lim_(x to oo) f(x)=0`
(iv) `f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3)`
(v) `f''(x) gt 0 AA x in (-oo,-2) uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo)`
Then answer the following questions
Find the Maximum possible number of solutions of `f(x)=|x|`

Text Solution

Verified by Experts

The correct Answer is:
3
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part II|22 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

Given f(x)=(ax+b)/(x+1), lim_(x to oo)f(x)=1 and lim_(x to 0)f(x)=2 , then f(-2) is

Let f(x) is a differentiable function everywhere and suppose lim_(x rarr oo)(f'(x)+3f(x))=12 then lim_(x rarr oo)f(x) is equal to

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt AA x in (-1,oo) also f '(-1)=0 given lim _(x to oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. The minimum number of points where f'(x) is zero is:

If f(x) is a differentiable function of x then lim_(h rarr0)(f(x+3h)-f(x-2h))/(h)=

If the function f (x) = {{:(3,x lt 0),(12, x gt 0):} then lim_(x to 0) f (x) =

If f(x)=(x^(2))/(1+x^(2)), prove that lim_(x rarr oo)f(x)=1

Let f(x) lt 0 AA x in (-=oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=o, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt AA x in (-1,oo) also f '(-1)=0 given lim _(x to oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equatin f (x)=x ^(2) is :

Let f :R to [0,oo) be such that lim_(xto3) f(x) exists and lim_(x to 3) ((f(x))^2-4)/sqrt(|x-3|)=0 . Then lim_(x to 3) f(x) equals

RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Let f(x) =sin ({x})/(a) + cos ({x})/(a) where a gt 0 and {.} denotes t...

    Text Solution

    |

  2. Consider the equation x^4+4x^3-8x^2+K=0. Answer the following (1) Th...

    Text Solution

    |

  3. A function f(x) having the following properties, (i) f(x) is conti...

    Text Solution

    |

  4. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

    Text Solution

    |

  5. If y=(a x+b)/((x-1)(x-4)) has a turning value at (2,\ -1) find a\ &...

    Text Solution

    |

  6. if A be the area of a triangle, prove that the error in A resulting fr...

    Text Solution

    |

  7. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

    Text Solution

    |

  8. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

    Text Solution

    |

  9. find the interval of increasing and decreasing for the function g...

    Text Solution

    |

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

    Text Solution

    |

  11. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  12. For any acute angled DeltaABC find the maximum value of (sin A)/(A) +(...

    Text Solution

    |

  13. For what real values of a' and 'b' all the extrema of the function f(x...

    Text Solution

    |

  14. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

    Text Solution

    |

  15. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |

  16. Find the cosine of the angle at the vertex of an isoceles triangl...

    Text Solution

    |

  17. A tangent to the curve y=1 -x^(3) is drawn so that the abscissa x(0)...

    Text Solution

    |

  18. A cone is made from a circular sheet of radius sqrt3 by cutting out a ...

    Text Solution

    |

  19. Find the minimum distance of origin from the curve ax^(2) +2bxy+ay^(2)...

    Text Solution

    |

  20. Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

    Text Solution

    |