Home
Class 12
MATHS
Let f(x)=max{|x^2-2|x| |, |x|} and g(x)=...

Let `f(x)=max{|x^2-2|x| |, |x|}` and `g(x)=min{|x^2-2|x| |, |x|}` then prove that f(x) in not differentiable at 5 points and g(x) is not differentiable at 7 points. Also draw the graph of both `f(x)` and `g(x)`.

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=max{|x^(2)-2|x||,|x|} and g(x)=min{|x^(2)-2|x||,|x|} then prove that f(x) in not differentiable at 5 points and g(x) is not differentiable at 7 points.Also draw the graph of both f(x) and g(x) .

Let f(x)=max.{|x^(^^)2-2|x||,|x|} and g(x)=min.{|x^(^^)2-2|x||,|x|} then

If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may be differentiable at x=a

Let f(x)=|x-1|+|x-2| and g(x)={min{f(t):0<=t<=x,0<=x<=3 and x-2,x then g(x) is not differentiable at

Let f(x)=|x| and g(x)=|x^(3)|, then f(x) and g(x) both are continuous at x=0 (b) f(x) and g(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0

Let f(x)=|x| and g(x)=|x^3|, then (a)f(x)a n dg(x) both are continuous at x=0 (b)f(x)a n dg(x) both are differentiable at x=0 (c)f(x) is differentiable but g(x) is not differentiable at x=0 (d)f(x) and g(x) both are not differentiable at x=0

f(x)=min({x,x^(2)} and g(x)=max{x,x^(2)}

Let f(x)={(-1, -2lexlt0),(x^2-1,0lexlt2):} if g(x)=|f(x)|+f(|x|) then g(x) in (-2,2) (A) not continuous (B) not differential at one point (C) differential at all points (D) not differential at two points

Let f(x)=sin x,g(x)={{max f(t),0 pi Then number of point in (0,oo) where f(x) is not differentiable is

RESONANCE DPP-JEE MAINS-All Questions
  1. If vec a= vec b+ vec c , vec bx vec dC= vec0 and vec cdot vec d=0 th...

    Text Solution

    |

  2. A rectangle PQRS has its side PQ parallel to the line y= mx and verti...

    Text Solution

    |

  3. Let f(x)=max{|x^2-2|x| |, |x|} and g(x)=min{|x^2-2|x| |, |x|} then pro...

    Text Solution

    |

  4. If alpha,beta be the roots of the equation (x-a)(x-b)+c=0(c!=0), then ...

    Text Solution

    |

  5. int(sinxcosx)/(sqrt(1-sin^4x)).dx

    Text Solution

    |

  6. If A+B+C=pi , then the value of the determinant D=|sin^2AcotA1sin^2Bc...

    Text Solution

    |

  7. lim(x->oo)(sqrt(x^4+ax^3+3x^2+b x+2)-sqrt(x^4+2x^3+cx^2+3x-d))=4

    Text Solution

    |

  8. For all real value of x , the maximum value of the expression x/(x^2-5...

    Text Solution

    |

  9. If minimum of f(x)=(a)/(x)+bx at x=2 is 2, then (a, b) -=….

    Text Solution

    |

  10. STATEMENT-1 : The graph of y=[sqrt(1-cos2x]) consists of only two line...

    Text Solution

    |

  11. P is a point on the line through the point A whose position vector i...

    Text Solution

    |

  12. ABC is an isosceles triangle. If the co-ordinates of the base are (1, ...

    Text Solution

    |

  13. lim(x->0) (1-cos x cos 2x cos 3x)/ (sin^2 2x) is equal to a) 3/4 b)...

    Text Solution

    |

  14. The straight line x-y-2=0 cuts the axis of x at Adot It is rotated ...

    Text Solution

    |

  15. The value of sin^(-1){cot(sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)(sqrt(1...

    Text Solution

    |

  16. The number solution of the equation sgn(x^2)=|x-2| is 1 (b) 0 (c) 2...

    Text Solution

    |

  17. The vectors vec a=3 veco-2 vec j+2 vec k and vec b=- vec i-2 vec k a...

    Text Solution

    |

  18. Number of roots of the equation 2sqrt(2x+1)=2x-1 is 0 (b) 1 (c) 2 (...

    Text Solution

    |

  19. If vec a= hat i+ hat j+ hat k& vec b= hat i-2 hat j+ hat i , then the...

    Text Solution

    |

  20. Find the integral solutions to the equation [x][y]=x+y . Show that all...

    Text Solution

    |