Let f: R arrow R be defined as, f(x) = begincases -55x, textif x 4, endcases Let A= x ∈ R: f is increasing . Then A is equal to

Question

Let f: R arrow R be defined as, f(x) = begincases -55x, textif x < -5 2x3 -3x2 -120x, textif 5 le x le 4 2x3 -3x2-36x-336& textif x > 4, endcases Let A= x ∈ R: f is increasing . Then A is equal to (A) (-∞,-5) ∪(4, ∞) (B) (-5, ∞) (C) (-∞,-5) ∪(-4, ∞) (D) (-5,-4)∪(4, ∞)

Tardigrade Admin · Accepted Answer

f'(x) = begincases -55; x < -5 6(x - 5)(x+4); -5 < x <4 6(x-3)(x+2); x > 4 endcases f ( x ) is increasing in x ∈(-5,-4) ∪(4, ∞)

Q. Let $f : R \to R$ be defined as,
$f (x) = ⎩ ⎨ ⎧ - 55 x, 2 x^{3} - 3 x^{2} - 120 x, 2 x^{3} - 3 x^{2} - 36 x - 336 if x < - 5 if 5 \leq x \leq 4 if x > 4,$
Let $A = {x \in R : f$ is increasing $} .$ Then $A$ is equal to

$(- \infty, - 5) \cup (4, \infty)$

$(- 5, \infty)$

$(- \infty, - 5) \cup (- 4, \infty)$

(-5,-4) $\cup (4, \infty)$

$f^{'} (x) = ⎩ ⎨ ⎧ - 55; 6 (x - 5) (x + 4); 6 (x - 3) (x + 2); x < - 5 - 5 < x < 4 x > 4$
$f (x)$ is increasing in $x \in (- 5, - 4) \cup (4, \infty)$

Q. Let f:R→R be defined as, f(x)=⎩⎨⎧​−55x,2x3−3x2−120x,2x3−3x2−36x−336​if x<−5if 5≤x≤4if x>4,​ Let A={x∈R:f is increasing }. Then A is equal to

(−∞,−5)∪(4,∞)

(−5,∞)

(−∞,−5)∪(−4,∞)

(-5,-4)∪(4,∞)