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I need to check whether I've done it correctly

  1. To find whether a point is maximum of function $f(x)$, we have to checked whether $f''(x)>0, f''(x)=0$ or $f''(x)<0?$

  2. To find the inflection point of the function, we have to find, $f''(x)=0, f'(x)=0,$ $f(x)=0.$

  3. When choose the value of $\sqrt{(64,3)},$ $X_o$ has the value: $64, 0,3$ or $X_o>64.$

My answers are the following.

$1. f''(x)<0$

$2. f''(x)=0$

$3. X_o = 64.$

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  • $\begingroup$ OP, check and see if my edit is what you wanted? $\endgroup$ – Lays Apr 22 '13 at 23:48
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Your first two answers are correct.

If you mean by $\sqrt{(64, 3)}$ that you need to find the value of $x_0$ in order to determine the distance of the point $(64, 3)$ from the origin, then you'd want $x_0 = 0$, the $x$-coordinate of the origin:

Distance = $\sqrt{(64 - 0)^2 + (3 - 0)^2}$.

But it will work equally well if we reverse the positions:

Distance = $\sqrt{(0 - 64)^2 + (0 - 3)^2}$. So $x_0 = 64$ works just as well.

But the value of the distance between $(64, 3)$ and $(0, 0)$ is $\sqrt{73}$.

So the answer for $(3)$ depends on what is meant by $x_0$.

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  • $\begingroup$ OP probably means linear approximation. $\endgroup$ – Halil Duru Apr 22 '13 at 23:58
  • $\begingroup$ Ohhh, okay, @Halil ..... If that's the case, then all is good. Thanks for clarifying! $\endgroup$ – amWhy Apr 22 '13 at 23:59
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    $\begingroup$ Thanks, I understand and I can't explain the Xo as English is not my native language but It's ok as 64! Thank you. $\endgroup$ – user2041143 Apr 22 '13 at 23:59
  • $\begingroup$ You're welcome! $\endgroup$ – amWhy Apr 23 '13 at 0:00
  • $\begingroup$ @amWhy: Obviously helped the OP + 1 $\endgroup$ – Amzoti Apr 23 '13 at 0:12

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