How do you find all critical point and determine the min, max and inflection given $f (x) = x^{2} - 8 x - 10$ $f(x)=x^2-8x-10$ ?

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How do you find all critical point and determine the min, max and inflection given $f (x) = x^{2} - 8 x - 10$ $f(x)=x^2-8x-10$ ?

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Answer 1 · 2016-10-16T08:53:23

At $x = 4$ $x=4$ is a minimum only

Explanation:

$f (x) = x^{2} - 8 x - 10$ $f(x)=x^2-8x-10$
Differentiating with respect to x, $f'(x)=2x-8$
Differentiating once more, $f''(x)=2$ which is $>0$ so we are expecting a minimum
When $f'(x)=0 => 2x-8=0 =>x=4$
When $x<4, f'(x) <0$
and when $x>4, f'(x)>0$
So we have a minimum
Check
$f(3)=3*3-8*3-10=-25$
$f(5)=5*5-8*5-10 =-25$
and $f(4)=4*4-8*4-10=-26$
So we have a min. only

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How do you find all critical point and determine the min, max and inflection given $f (x) = x^{2} - 8 x - 10$ $f(x)=x^2-8x-10$ ?

1 Answer

Explanation:

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Science

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Humanities

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How do you find all critical point and determine the min, max and inflection given f(x)=x^2-8x-10f(x)=x2−8x−10f(x)=x^2-8x-10?

1 Answer

Explanation:

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How do you find all critical point and determine the min, max and inflection given $f (x) = x^{2} - 8 x - 10$ $f(x)=x^2-8x-10$ ?