Find the minimum value of a, such that function $f (x) = x^{2} + a x + 5$ , is increasing in interval $[1, 2]$ .

Open in App

Solution

$\begin{matrix} f (x) = x^{2} a x + 5 d i f f e r e n t i a t e w i t h r e s p e c t t o x \Rightarrow f (x) = 2 x + a \Rightarrow f (x) > 0 \Rightarrow 2 x + a > 0 a > - 2 x P u t x - 1 ∴ min i m u m v a l u e o f i s - 2 \times 1 = - 2 \end{matrix}$

Suggest Corrections

Similar questions

Find the least value of a such that the function f given is strictly increasing on [1, 2].

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

R

a

f (x) = x^{2} + a x + 1

[1, 2]

S

a

f (x) = x^{2} + a x + 1

[1, 2]

| R - S |

a

x^{2} + a x + 1

[1, 2]

f (x) = x^{2} - a x + 4

(2, + \infty)

a

Join BYJU'S Learning Program