Answer:
minimum value of function is [tex]\frac{45}{8}[/tex] .
Step-by-step explanation:
Given function represents a parabola.
Now, here coefficient of [tex]x^{2}[/tex] is positive , so the parabola will be facing upwards and thus the function will be having a minimum.
Now, as we know that minimum value of a parabolic function occurs at
x = [tex]\frac{-b}{4a}[/tex] .
Where , b represents the coefficient of x and a represents the coefficient of [tex]x^{2}[/tex] .
here, a = 2 , b = -6
Thus [tex]\frac{-b}{4a}[/tex] = [tex]\frac{6}{8}[/tex]
= [tex]\frac{3}{4}[/tex]
So, at x = [tex]\frac{3}{4}[/tex] minimum value will occur and which equals
y = 2×[tex]\frac{9}{16}[/tex] - [tex]\frac{18}{4}[/tex] + 9 = [tex]\frac{45}{8}[/tex] .
Thus , minimum value of function is [tex]\frac{45}{8}[/tex] .
