Home
Class 12
MATHS
Statement I :The function f(x)=(x^(3)+3x...

Statement I :The function `f(x)=(x^(3)+3x-4)(x^(2)+4x-5)` has local extremum at x=1.
Statement II :f(x) is continuos and differentiable and f'(1)=0.

A

Statement I is true, Statement II is also true, Statement II is the correct explanation of statement I.

B

Statemetn I is true, Statement II is also true, Statement II is not correct explanation of Statement I

C

Statement I is true, Statement II is false

D

Statement I is false, Statement II is true

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|35 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=(4-x^(2))/(4x-x^(3)) is

The function f (x) = (x)/(2) + (2)/(x) has a local minimum at :

Let f(x)=ln(2+x)-(2x+2)/(x) . Statement I The function f(x) =0 has a unique solution in the domain of f(x). Statement II f(x) is continuous in [a, b] and is strictly monotonic in (a, b), then f has a unique root in (a, b).

bb"Statement I" The equation f(x)=4x^(5)+20x-9=0 has only one real root. bb"Statement II" f'(x)=20x^(4)+20=0 has no real root.

True or False statements: Fermat Theorem If a function f has a local extremum at x = c, then f" (C ) = 0.

Differentiation of the function : f(x) = 4x+3

If a function f(x) has a local extremum at a point x = c, then what can be said about f' (c)?

Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a

Consider f(x)=(x)/(x^(2)-1) Statement I Graph of f(x) is concave up for xgt1. Statement II If f(x) is concave up then f''(x)gt0

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Statement I :The function f(x)=(x^(3)+3x-4)(x^(2)+4x-5) has local ext...

    Text Solution

    |

  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) to vec R be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , ...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

    Text Solution

    |

  7. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  8. A vertical line passing through the point (h,0) intersects th ellipse ...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. The total number of local maxima and local minima of the function f(x)...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  15. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which has local maximum at x=-1 . If f(2)...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |