Sketch the graph of f(x) if ...f'(x)>0 on (2,4) and f'(x)<0 on (−∞, 2) ∪ (4, ∞),f''(x)>0 on (1, 3) ∪ (5, ∞) and f''(x)<0 on (−∞, 1) ∪ (3, 5), and f(x) ->0 as x->±∞

2. Sketch the graph of one function g that is continuous on [-4, 4] and has all of the following properties: (a) g(-4) = 1 = g(4) (b) g(-2) = 3 = maximum value of g on [-4,4] (c) g(2) = –1 = minimum value of g on [-4, 4]. (d) g'(0) = 0 (so 0 is a critical number of g), but g(0) is not an extreme value of g.

Help cubic function whose graph has horizontal tangents at (-2,6) and -- +5)=(OH • A 2 (2₁0). { y = ax ²³ + bx²² textd ах {Y= 1 X Y D(-2,6) (5) 6 f(2)=3ax²²³² +2bx+c =3a (2)² + 2b (2) tr 12a + 4b +c 3 Y = ax²³ + bxc²+cx + d 3 Y = ax² +bx² +ex td 3 6= a (-2)²³ + b (-2)² + (-2) + d (0= a (2) ²³+ b(2)³² + c(2) + d 0= 8a + 4b + 2 c + d 6=-8a + 4b - 2c + d 3 2 Y' (₂c) = ax²³ + bxc² +cx +d (ƒ(-2)=3ax²³² +2bx te 2 = a (3x²)+b(2x) + c(1) "3a (-2)² + 2b (-2) + C 2 = 3ax² +2bx te 8b+2d=6 8(0) + 2d=6 2d=6 622 d= 2 d = 3 YEW 1 +6=0 98a + 4b +2c tα = 0 X Y →→ (2.0) 8a-24a +3=0 -16 α = -3 -3 a=-16 3 а a = 16 -8a+4b-2x+d+86 +46+2c+d=6) 26=0 Jr) (³€+ N)=(3rk 4b+d+4b+d=6²² +²b = 2 b=2=6² b=0=₁ 8a +4(0) + 2 (-12a) +3=0 (2) 12a + 2b +c f(-2) s - 112a + 4b + c = (12a + 2b + c) = 0 12a + 4b+R-12a-2bx=0 2x604b =26=0m ³7 37 7₁ (10) 12a + 2b + c =0 -12a + 2(0)+c=0 12a+c=0 1)C=-12 au c=²=12a (²3² + 1) = (2x (c==12 (²76) 36 C = 76 -A= q 2 Y=ar² thre² textd 3 3 2 = nove +60₂e²+ ( ahe +3 2 3 3 = 16x² - 4x +3 льк

Sketch a graph of the function f(0) = 2 cos os(- -Зл -5л/2 - 2л -3л/2 -40 -) 171) +3 2 -П -П/2 6 5 4 3 2 1 -1 -2 -3 -4 -5- -6- П/2 П 3/2 2л 5л/2 Зл