Question

please write clearly

2.) Sketch the graph of a function that satisfies all of the given conditions f(0) = f'(4) = 0, f'(x) = 1 if x < -1, f'(x) > 0 if 0 < x < 2, f'(x) < 0 if-1<x<0 or 2 <x< 4 or x > 4, lim f'(x) = 0, lim '(x) = -0, f"(x) > 0 if -1 < x < 2 or 2 <x< 4, f"(x) < 0 if x > 4 1-2

Answer 1

Giren → → condition f'lo) = f'(4) = 0 which means of x=0,4 cuore have horizontal tangent line -slope is zero or have point of inflection (at x=0,4). f'(x) = + (positive) for for (sea-1 (constant), flow is straight line and it is increasing for a <-1 or • f'(x) <0 (negative) for 1-1<x<0 2<x<4 OY x>4 which means frus is decreasi reasing for x € (-1,0) 01344) (410) (positive) lim f'(x) = slope o infinite at x = 27 42- bojust before lim f'(o) '(o) = -1 slope have infhinfinite (negative) (function decreasiy). f"(n) >0 con care upward for at (-1, 2)| (2,4). { n=2 U-2+ f"lu) <0 con care downward for x =(4,0)

Y concave upward, -fin) is decrewing concare upward point of inflection. f'(4)=0. f'(o)=0 x=4 n=0 x=2. X=-1 concave downward. fin) is increasing