(adsbygoogle = window.adsbygoogle || []).push({}); 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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# Differentiation problem!

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