Home
Class 12
MATHS
If f(x) = 3(2x + 3)^(2//3) + 2x + 3, the...

If `f(x) = 3(2x + 3)^(2//3) + 2x + 3`, then:
(a) `f(x)` is continuous but not differentiable at `x = - (3)/(2)`
(b) `f(x)` is differentiable at `x = 0`
(c) `f(x)` is continuous at `x = 0`
(d) `f(x)` is differentiable but not continuous at `x = - (3)/(2)`

A

(a) `f(x)` is continuous but not differentiable at `x = - (3)/(2)`

B

(b) `f(x)` is differentiable at `x = 0`

C

(c) `f(x)` is continuous at `x = 0`

D

(d) `f(x)` is differentiable but not continuous at `x = - (3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise EXERCISE 4|3 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|50 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Show that f(x) = |x - 5| is continuous but not differentiable at x = 5.

Show that f(x) = |x-3|, x in R is continuous but not differentiable at x =3.

"Let "f(x)=phi(x)+Psi(x) where, phi'(x) and Psi'(x) are finite and definite. Then, a. f(x) is continuous at x = a b. f(x) is differentiable at x = a c. f'(x) is continuous at x = a d. f'(x) is differentiable at x = a

If f(x) be such that f(x) = max (|3 - x|, 3 - x^(3)) , then (a) f(x) is continuous AA x in R (b) f(x) is differentiable AA x in R (c) f(x) is non-differentiable at three points only (d) f(x) is non-differentiable at four points only

Let f(x) =int_0^1|x-t|t dt , then A. f(x) is continuous but not differentiable for all x in R B. f(x) is continuous and differentiable for all x in R C. f(x) is continuous for x in R-{(1)/(2)} and f(x) is differentiable for x in R - {(1)/(4),(1)/(2)} D. None of these

Show that f(x) = {:{(|2x-3|[x],xge1),(sin((pix)/(2)), x <1):} is continuous but not differentiable at x =1.

Let f(x) = int_(-2)^(x)|t + 1|dt , then a. f(x) is continuous in [-1, 1] b. f(x) is differentiable in [-1, 1] c. f'(x) is continuous in [-1, 1] d. f'(x) is differentiable in [-1, 1]

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

Let f(x)= sin^(-1)((2x)/(1+x^2))AAx in R . The function f(x) is continuous everywhere but not differentiable at x is/ are

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)
  1. If f(x) = |x+1|(|x|+|x-1|), then at what point(s) is the function not ...

    Text Solution

    |

  2. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

    Text Solution

    |

  3. If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...

    Text Solution

    |

  4. f(x) = cos x and H(x) = {{:(min{f(t), 0 le t lt x},0 le x le (pi)/(2))...

    Text Solution

    |

  5. If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then: (a) f(x) is continuous but ...

    Text Solution

    |

  6. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

    Text Solution

    |

  7. if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} ...

    Text Solution

    |

  8. Let [x] denote the greatest integer less that or equal to x. If f(x) =...

    Text Solution

    |

  9. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

    Text Solution

    |

  10. The function f(x)=sqrt(1-sqrt(1-x^2)) a. has its domain -1 le x le 1 ...

    Text Solution

    |

  11. Consider the function f(x) = |x^(3) + 1|. Then,

    Text Solution

    |

  12. f is a continuous function in [a,b]; g is a continuous function in [b,...

    Text Solution

    |

  13. Which of the following function(s) has/have the same range ?

    Text Solution

    |

  14. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

    Text Solution

    |

  15. Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0...

    Text Solution

    |

  16. A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0)...

    Text Solution

    |

  17. Let f(x) = int(-2)^(x)|t + 1|dt, then a. f(x) is continuous in [-1, ...

    Text Solution

    |

  18. A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...

    Text Solution

    |

  19. Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 )...

    Text Solution

    |

  20. If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x...

    Text Solution

    |