Let f(x)= begincases2-|x2+5 x+6|, x ≠-2 b2+1, x=-2 endcases. If f(x) has relative maximum at x=-2, then the range of the b, is

Question

Let f(x)= begincases2-|x2+5 x+6|, x ≠-2 b2+1, x=-2 endcases. If f(x) has relative maximum at x=-2, then the range of the b, is (A) | b | ≥ 1 (B)  mid b mid< 1 (C) b >1 (D) b < 1

Tardigrade Admin · Accepted Answer

As, f(x) has relative maximum at x=-2, So f(-2) ≥ undersetx arrow-2 textLim f(x) ⇒ b 2+1 ≥ underset x arrow-2 textLim (2-| x 2+5 x +6|) ⇒ b 2 ≥ 1 ⇒| b | ≥ 1

Q. Let $f (x) = {2 - ∣ ∣ x^{2} + 5 x + 6 ∣ ∣, b^{2} + 1, x \neq = - 2 x = - 2$ . If $f (x)$ has relative maximum at $x = - 2$ , then the range of the $b$ , is

$∣ b ∣ \geq 1$

$∣$ b $∣< 1$

$b > 1$

b $< 1$

As, $f (x)$ has relative maximum at $x = - 2$ ,
So $f (- 2) \geq x \to - 2 Lim f (x)$
$\Rightarrow b^{2} + 1 \geq x \to - 2 Lim (2 - ∣ ∣ x^{2} + 5 x + 6 ∣ ∣)$
$\Rightarrow b^{2} \geq 1 \Rightarrow ∣ b ∣ \geq 1$

Q. Let f(x)={2−∣∣​x2+5x+6∣∣​,b2+1,​x=−2x=−2​. If f(x) has relative maximum at x=−2, then the range of the b, is

∣b∣≥1

∣ b ∣<1

b>1

b <1