What is the stationary point and its nature for the function f(x) = x^2-8x+4?

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Question:
For the graph [tex]x^2-8x+4[/tex] :
(i) find the coordinates of the stationary point;
(ii) say, with reasoning, weather this is a maximum or minimum point;
(iii) check your answer by using the method of 'completing the square' to find the vertex;
(iv) state the range of values which the function can take.

Attempt:
(i) [tex]f(x) = x^2-8x+4[/tex]
[tex]f'(x) = 2x-8[/tex]
[tex]f'(x) = 0[/tex]
[tex]2x-8 = 0[/tex]
[tex]2x = 8[/tex]
[tex]x = \frac{8}{2} = 4[/tex]

[tex]f(x) = x^2-8x+4[/tex]
[tex]f(x) = 4^2-8\times4+4[/tex]
[tex]f(x) = -12[/tex]

Stationary Point = [tex](4,-12)[/tex]

(ii) [tex]f'(1) = 2x-8[/tex]
[tex]f'(1) = 2(1)-8[/tex]
[tex]f'(1) = -6[/tex]

[tex]f'(7) = 2x-8[/tex]
[tex]f'(7) = 2(7)-8[/tex]
[tex]f'(7) = 6[/tex]

[tex]x \leq 4[/tex]
Minimum Point

(iii) Need help...
 
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