Què és el vèrtex de y = (x - 3) ^ 2 + x ^ 2-4x + 3?

Resposta:

# (2.5, -0.5) min #

Explicació:

# y '= 2 (x-3) * 1 + 2x-4 #

# => 2x-6 + 2x-4 #

# => 4x-10 #

# => 2 (2x-5) # #

# y '= 0 #

#=>#

# 2 (2x-5) = 0 #

# => 2x-5 = 0 #

# => 2x = 5 #

# => x = 5/2 = 2,5 #

#y '' = 4> 0 => min

#y_ ((2.5)) = (2.5-3) ^ 2 + (2.5) ^ 2-4 (2.5) + 3 = #

#=(-0.5)^2+(2.5)^2-10+3#

#=0.25+6.25-7#

#=-0.5#

# (2.5, -0.5) min #