Answer:
f(x) has a minimum value is zero at [tex]x = \frac{1}{2}[/tex]
Step-by-step explanation:
Explanation:-
step(i):-
Given function y =f(x)= x² - x + 1/4 ....(i)
Differentiating equation (i) with respective to 'x', we get
[tex]y^{l} =\frac{d y}{d x} = 2 x -1 +0[/tex] ...(ii)
Equating Zero 2 x - 1 = 0
[tex]2 x = 1[/tex]
[tex]x = \frac{1}{2}[/tex]
Step(ii):-
Again differentiating with respective to 'x', we get
[tex]y^{ll} =\frac{d^2 y}{d x^2} = 2 (1) >0[/tex]
f(x) has a minimum value at [tex]x = \frac{1}{2}[/tex]
Step(iii):-
y =f(x) = x² - x + 1/4
Put [tex]x = \frac{1}{2}[/tex]
[tex]f( \frac{1}{2}) = (\frac{1}{2} )2-\frac{1}{2} +\frac{1}{4}[/tex]
[tex]f(\frac{1}{2} ) = \frac{2}{4} -\frac{1}{2}[/tex]
[tex]f(\frac{1}{2} ) = 0[/tex]
f(x) has a minimum value is zero at [tex]x = \frac{1}{2}[/tex]
