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Hello.
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So here we want to find the polynomial of order 3 for our function f of x.
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So here f of x is equal to the square root of x.
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And while of order 3, we have p sub 3 of x is equal to our function evaluated at a.
00:19
So our given a is equal to 2.
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And then plus the first derivative evaluated at a times x minus a.
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And then plus the second derivative evaluated at a over 2 factorial times x minus a.
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Squared and then plus the third derivative evaluated at a over three factorial times x minus a to the third so we just take our function and we evaluate at a so our function is f of x is equal to the square root of x okay so we first find what is f of two well f of two is just equal to the square root of two right because our function is square of x so f of two is equal to the square root of 2.
01:01
Now, our first derivative is then going to be 1 over 2 times square root of x.
01:08
So the first derivative, f prime, evaluated at 2, is going to be equal to 1 over 2 times the square root of 2.
01:18
Then our second derivative evaluated at 2, so our second derivative is going to be equal to a negative 1 4th times x to the negative three halves.
01:30
So then evaluating at 2, we should be getting a negative square root of 2 over 16.
01:39
And then the third derivative, again, evaluated at 2.
01:45
So our third derivative is going to be 3x times x to the negative 5 halves power...