Taylor Polynomial State the definition of an n th-degree Taylor polynomial of f centered at c.
The statement for the definition of an nth-degree Taylor polynomial of a function centered at .
Let a function is such that is can be written as a polynomial of nth-degree whose graph resemble the graph of the function near a point . The nth-degree polynomial is given by,
There are certain requirement that the above polynomial must satisfy such that the graph of the polynomial must passes through the point and the slope of the polynomial near that point must be same as that of the slope of the function at that point. Therefore, the derivatives of the polynomial at the considered point must be equal to the corresponding derivatives of the function at the same point.
Differentiate the polynomial times and find all of its derivatives.
Now, find the value of the above derivatives at
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