Home
Class 12
MATHS
Find the least value of ' a ' such that ...

Find the least value of `' a '` such that the function `f(x)=x^2+a x+1` is increasing on `[1,\ 2]` . Also, find the greatest value of `' a '` for which `f(x)` is decreasing on `[1,\ 2]` .

Text Solution

Verified by Experts

`f'(x)=2x+a`
Now, function f will be increasing in `(1, 2)`, if `f'(x)>0` in `(1, 2)`.
`f'(x)>0=>2x+a>0`
`x> -a/2`
Therefore, we have to find the least value of a such that Thus, `x> -a/2`, when `x in (1, 2)`
Thus, the least value of a for f to be increasing on `(1, 2)` is given by,
`-a/2=1=>a=-2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

Similar Questions

Explore conceptually related problems

Find the least value of a such that the function f given by f(x)=x^(2)+ax+1 is strictly increasing on (1,2)

the function f(x)=x^2-x+1 is increasing and decreasing

Knowledge Check

  • The set of values of a 'for which the function f (x) = x^2 + ax +1 is an increasing function on [1,2] is

    A
    `(-oo ,-4)`
    B
    ` [-4,oo)`
    C
    `[4,oo)`
    D
    ` (-oo ,4)`

  • If f(x) = x^(2) + kx + 1 is increasing function in the interval [ 1, 2], then least value of k is –

    A
    2
    B
    4
    C
    -2
    D
    -4

    • Similar Questions

    Explore conceptually related problems

    If yR' is the least value of 'a' such that the function f(x) = x^(2) + ax +1 is increasing on [1, 2] and 'S' is the greatest value of ' a' such that the function f(x) = x^(2) + ax +1 is decreasing on [1, 2], then the value of |R — S| is_____________

    Find the greatest value of the function f(x)=(2)/sqrt(2x^(2)-4x+3)

    Find the least value of k for which the function x^(2)+kx+1 is an increasing function in the interval 1

    Find the values of x for which the functions f(x)=3x^(2)-1 and g(x)=3+x are equal

    Find the least value of k for which the function x^2+kx+1 is an increasing function in the interval 1 < x <2

    Find the intervals in which the function f(x)=log(1+x)-(2x)/(2+x) is increasing or decreasing.

    Home
    Profile