Let f : R → R be defined as f x = - 55 x , if x - 5 2 x 3 - 3 x 2 - 120 x , if - 5 ≤ x ≤ 4 2 x 3 - 3 x 2 - 36 x - 336 , if x 4 Let A = { x ∈ R : f is increasing}. Then A is equal to:

Question

Let f : R → R be defined as f x = - 55 x , if x - 5 2 x 3 - 3 x 2 - 120 x , if - 5 ≤ x ≤ 4 2 x 3 - 3 x 2 - 36 x - 336 , if x > 4 Let A = { x ∈ R : f is increasing}. Then A is equal to:, - 5 , ∞, - 5 , - 4 ∪ 4 , ∞, - ∞ , - 5 ∪ - 4 , ∞, - ∞ , - 5 ∪ 4 , ∞

MARKS App · Accepted Answer

f x = - 55 x , if x - 5 2 x 3 - 3 x 2 - 120 x , if - 5 ≤ x ≤ 4 2 x 3 - 3 x 2 - 36 x - 336 , if x > 4 f ' x = - 55 , if x - 5 6 x 2 - 6 x - 120 , if - 5 ≤ x ≤ 4 6 x 2 - 6 x - 36 , if x > 4 f ' x = - 55 ; x - 5 6 x - 5 x + 4 ; - 5 x 4 6 x - 3 x + 2 ; x > 4 f x is increasing ⇒ f ' x > 0 So, x ∈ - 5 , - 4 ∪ 4 , ∞

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