Question

determine o valor máximo ou mínimo das funções dadas por: a) f(x) = 3x² + 2xb) f(x) = 2x² - 5x + 3c) f(x) = x² - 40x + 800por favor me ajudem

Answer 1

max: a<0
min: a>0

a) 3x^2+2x
xv= -b/2a
xv= -2/2.3
xv= -2/6
xv= -1/3

yv= f(xv)
yv= f(-1/3)
yv= 3(-1/3)^2+2.1/3
yv= 3.1/9+2/3
yv= 3/9+2/3
yv= 1/3+2/3
yv= 3/3
yv= 1

v(-1/3, 1)


b) 2x^2-5x+3
xv= -b/2a
xv= -(-5)/2.2
xv= 5/4

yv= f(xv)
yv= f(5/4)
yv= 2.(5/4)^2-5.5/4+3
yv= 2.25/16-25/4+3
yv= 50/16-25/4+3
yv= 25/8(1)-25/4(2)+3/1(8)
yv= 25/8-50/8+24/8
yv= -1/8

v(5/4, -1/8)

c) x^2-40x+800

xv= -b/2a
xv= -(-40)/2.1
xv= 40/2
xv= 20

yv= f(xv)
yv= f(20)
yv= 20^2-40.20+800
yv= 400-800+800
yv= 400

v(20, 400)