Question

The minimum value of f (x) = x² - 6x + 10
Not use derivative

Answer 1

F (x) = x² - 6x + 10

therefore :
A = 1
B = -6
C = 10

D = b² - 4ac
     = -6² - 4 (1) (10)
     = 36 - (40)
     = -4

Minimun value:
Y min = D / -4a
           = -4 / -4 (1)
           = 1

So the minimum value of f (x) = x² - 6x + 10 is 1

Answer 2

x^2-6x+10. Easiest way to find minimum value is by factorizing it to a perfect square. It can be written as x^2-6x+9+1 which is equal to (x-3)^2+1. The minimum value of the square term is 0, that is when x=3 (as square number is always positive, minimum value it can take is zero). So, minimum value of the whole function is when x=3, and that is 1.