What Steps Are Needed to Determine Coefficients in a Taylor Polynomial?

[jlmccart03]

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

I got my test back and was unable to ask the professor, but how does one solve this problem specifically? I am posting an image of the entire page so you can see my original answers. I just don't know how you determine from the graph and all.

 

[Mark44]

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

I got my test back and was unable to ask the professor, but how does one solve this problem specifically? I am posting an image of the entire page so you can see my original answers. I just don't know how you determine from the graph and all.

Nowhere in your work are you using the given information that this is a Taylor polynomial, which is defined in terms of the function f and its derivatives. Because it's given that the polynomial is centered at 0, and since the Taylor polynomial is of degree 3, the polynomial will be in terms of f(0), f'(0), f''(0), and f'''(0).

The a) part has nothing to do with a minimum point on the graph. It has everything to do with the fact that the graph has a y-intercept of -2. The b) part has to do with what is the coefficient of x in the Taylor polynomial.

 

[jlmccart03]

Nowhere in your work are you using the given information that this is a Taylor polynomial, which is defined in terms of the function f and its derivatives. Because it's given that the polynomial is centered at 0, and since the Taylor polynomial is of degree 3, the polynomial will be in terms of f(0), f'(0), f''(0), and f'''(0).

The a) part has nothing to do with a minimum point on the graph. It has everything to do with the fact that the graph has a y-intercept of -2. The b) part has to do with what is the coefficient of x in the Taylor polynomial.

Does every question that's asks about the first coefficient deal with finding a y intercept? Also for part b: what are the necessary steps to obtain the coefficient? I guess I am confused on how you find solid numbers when given a polynomial with just letters and x. Thanks for the help your giving btw.

 

[Mark44]

Does every question that's asks about the first coefficient deal with finding a y intercept?

That's too broad a question to answer with a yes or no.

Also for part b: what are the necessary steps to obtain the coefficient? I guess I am confused on how you find solid numbers when given a polynomial with just letters and x.

You are given that $T_3(x) = a + bx + cx^2 + dx^3$. If you were given an equation y = f(x), what is theTaylor polynomial of degree 3?