Home
Class 12
MATHS
Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then ...

Let `f(x)=xsqrt(4a x-x^2),(a >0)dot` Then `f(x)` is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in`(5a ,oo)` (c). increasing in `(0,4a)` (d). none of these

A

increasing in (0,3a) decreasing in (3a,4a)

B

increasing in (a,4a),decreasing in `(5a,oo)`

C

increasing in `(0,4a)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1
f(X)=`xsqrt(4ax-x^(2))`
`therefore f(X) =sqrt(4ax-x^(2))+x(4a-2x)/2sqrt(4ax-x^(2))`
`=(2x(3a-x))/sqrt(4ax-x^(2))`
Now if `f(X)gt0` then
`2x(3a-x)gt0`
`2x(x-3a)lt0`
or x in (0,3a)
Thus f(x) increases in (0,3a) and decreases in (3a,4a)
Thus f(X) increases in (0,3a) and decreases (3a,4a)
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|48 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Numerical Value Type|24 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.7|5 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

If f(x)=xe^(x(x−1)) , then f(x) is (a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

If f(x)=x e^(x(x-1)) , then a) f(x) is increasing on [-1/2,1] b) decreasing on R c) increasing on R (d) decreasing on [-1/2,1]

Show that f(x)=sinx is increasing on (0,\ pi//2) and decreasing on (pi//2,\ pi) and neither increasing nor decreasing in (0,\ pi) .

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)

Show that f(x)=cosx is decreasing function on (0,pi), increasing in (-pi,0) and neither increasing nor decreasing in (-pi,pi)dot

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)

Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

f: RvecR ,f(x) is differentiable such that f(f(x))=k(x^5+x),k!=0)dot Then f(x) is always increasing (b) decreasing either increasing or decreasing non-monotonic

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasing.

CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
  1. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  2. The function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (...

    Text Solution

    |

  3. Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,...

    Text Solution

    |

  4. Function f(x)=|x|-|x-1| is monotonically increasing when (a) x<0 (b) ...

    Text Solution

    |

  5. If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , ...

    Text Solution

    |

  6. The length of the largest continuous interval in which the function f(...

    Text Solution

    |

  7. f(x)=(x-2)|x-3| is monotonically increasing in (-oo,5/2)uu(3,oo) (b)...

    Text Solution

    |

  8. f(x)=(x-8)^4(x-9)^5,0lt=xlt=10 , monotonically decreases in (a) (76/9...

    Text Solution

    |

  9. For all x in (0,1) (a) e^x<1+x (b) (log)e (1+x) < x (c) sin x > x (d) ...

    Text Solution

    |

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

    Text Solution

    |

  11. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then

    Text Solution

    |

  12. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

    Text Solution

    |

  13. Let f: RvecR be a function such that f(x)=a x+3sinx+4cosxdot Then f(x)...

    Text Solution

    |

  14. Which of the following statement is always true? If f(x) is increasing...

    Text Solution

    |

  15. Let f: RvecR be a differentiable function for all values of x and has ...

    Text Solution

    |

  16. Let f: Rvec be a differentiable function AAx in R . If the tangent dr...

    Text Solution

    |

  17. Let f(x) be a function such that f^(prime)(x)=(log)(1/3)[(log)3(sinx+a...

    Text Solution

    |

  18. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

    Text Solution

    |

  19. f(x)=|x loge x| monotonically decreases in (0,1/e) (b) (1/e ,1) (1,o...

    Text Solution

    |

  20. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

    Text Solution

    |