Home
Class 12
MATHS
If f '(x) phi (x) (x-2) ^(2). Were phi(2...

If `f '(x) phi (x) (x-2) ^(2).` Were `phi(2) ne 0 and phi (x)` is continuous at `x =2` then in the neighbouhood of `x =2`

A

f is increasing if `phi (2) lt 0`

B

f is decreasing if `phi (2) gt0`

C

f is neither increasing nor decreasing

D

f is increasin if `phi(2) gt 0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )|29 Videos
  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|15 Videos
  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(x-x_(0)) phi (x) and phi(x) is continuous at x= x_(0) . Then f'(x_(0)) is equal to

If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, then

If f(x)=x^(3)-x and phi (x)= sin 2x , then

If f(x) = {{:((x^(2)-(a+2)x+2a)/(x-2)",",x ne 2),(" "2",",x = 2):} is continuous at x = 2, then a is equal to

f(x)={(2|x|+x^2)/x ,\ \ \ x!=0 ,\ \ \ and 0 at x=0 is continuous at x = 0 or not.

If phi (x)=phi '(x) and phi(1)=2 , then phi(3) equals

If f(x)={{:((sqrt(x^(2)+5)-3)/(x+2)",",x ne-2),(k,","x=-2):} is continuous at x=-2 , then the value of k is

Let the function f(x)=x^(2)sin((1)/(x)), AA x ne 0 is continuous at x = 0. Then, the vaue of the function at x = 0 is

If phi (x) =int_(1//x)^(sqrt(x)) sin(t^(2))dt then phi ' (1)is equal to

if y+x(dy)/(dx)=x(phi(xy))/(phi'(xy)) then phi(xy) is equation to

VK JAISWAL ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f '(x) phi (x) (x-2) ^(2). Were phi(2) ne 0 and phi (x) is continuo...

    Text Solution

    |

  2. A conical vessel is to be prepared out of a circular sheet of metal of...

    Text Solution

    |

  3. On [1,e], then least and greatest vlaues of f (x) = x^(2)ln x are m a...

    Text Solution

    |

  4. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  5. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

    Text Solution

    |

  6. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  7. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  8. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  9. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  10. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  11. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  12. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  13. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

    Text Solution

    |

  14. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  15. The least positive vlaue of the parameter 'a' for which there exist at...

    Text Solution

    |

  16. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

    Text Solution

    |

  17. A tank contains 100 litres of fresh water. S solution containg 1 gm/li...

    Text Solution

    |

  18. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  19. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  20. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  21. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |