Question

please need answers as soon as possible with clear explanation thankyou.

il Bell 91% 1:41 PM a urwork3.edbian.org Problem 6. Remaining time: 94:20 (min:Sec) (9 points) Suppose that f(x) = (1 - x)(x + 1)2. (A) Find all critical values of f. Critical value(s) = (B) Use interval notation to indicate where f(x) is increasing. Increasing: (C) Use interval notation to indicate where f(x) is decreasing. Decreasing: (D) Find the x-coordinates of all local maxima of f. Local maxima at x = (E) Find the x-coordinates of all local minima of f. Local minima at x =

Answer 1

f(x) = (1-x)(1+1) om f'( na (n+12 (31-1) f" () = -61-2 Te For critical values, f'(n)=0 :-(4+12(31-1)=0 22-1, 12 - ģ (-ve) (+ve) (-ve) 09 Fig: - (diagram for f(n)) ve f(a) is increasing When f'(0) > 0 ilie (13) lie. at nat = + 1 / 3 f(m) is decreasing when f'( m20 (- 0,-1) UC,) f"(W): -66%)-2--2-2--4 Negative u ý n=-1, f"(2=-61-1)-2 = 6-2-4 = positive so, Local Minima for inflection puent, f"(-O -64-2=0 su, Local Maxima 따 at at 2-1 (2= 1/3 (+ve) (ve) ve) Lve ti) is Concave up when [Figi fos + "()] f"(12 >o (-0,3) down when f (4720 (-5,00) fin) is Concave

2 f(x) = (iam (*+1) LA) critical values : x=-1,5 (B) interval where increasing t', 1/3) (c) interval where decreasing |--,-1)U(+,-) () Local Maxima (E) لی ها Minima at (E) Concave up -3) (G) Concave down 65,00) (H) inflection puent -انی (1)