Question

2√(2x+8) (x+5)=36-3x​

Answer 1

Step-by-step explanation:

Given as f(x) = 8 + 36x + 3x2 – 2x3 Differentiate with respect to x f'(x) = (d/dx)(8 + 36x + 3x2 - 2x3) ⇒ f’(x) = 36 + 6x – 6x2 For the f(x) we have to find critical point, we must have ⇒ f’(x) = 0 ⇒ 36 + 6x – 6x2 = 0 ⇒ 6(–x2 + x + 6) = 0 ⇒ 6(–x2 + 3x – 2x + 6) = 0 ⇒ –x2 + 3x – 2x + 6 = 0 ⇒ x2 – 3x + 2x – 6 = 0 ⇒ (x – 3) (x + 2) = 0 ⇒ x = 3, – 2 It is clear, f’(x) > 0 if –2 < x < 3 and f’(x) < 0 if x < –2 and x > 3 Hence, f(x) increases on x ∈ (–2, 3) and f(x) is decreasing on interval (–∞, 2) ∪ (3, ∞)Read more on Sarthaks.com - https://www.sarthaks.com/641717/find-the-intervals-in-which-the-functions-are-increasing-or-decreasing-f-x-8-36x-3x-2-2x-3