Find-the-maximun-and-minimum-values-of-the-function-f-x-x-2-8x-7-and-sketch-its-graph-

Question Number 69355 by cesar.marval.larez@gmail.com last updated on 22/Sep/19

F i n d t h e m a x i m u n a n d m i n i m u m

v a l u e s o f t h e f u n c t i o n f (x) = x^{2} - 8 x + 7

a n d s k e t c h i t s g r a p h

Answered by MJS last updated on 22/Sep/19

\min / \max at f^{'} (x) = 0

to sketch it we also need the zeros

zeros

x^{2} - 8 x + 7 = 0

x = - \frac{p}{2} \pm \sqrt{\frac{p^{2}}{4} - q}

p = - 8; q = 7

x = 4 \pm \sqrt{16 - 7}

x_{1} = 1

x_{2} = 7

\min

f^{'} (x) = 2 x - 8 = 0 \Rightarrow x = 4

f^{″} (x) = 2 > 0 \Rightarrow minimum at (\begin{matrix} 4 \\ - 9 \end{matrix})

now sketch it

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