# Thread: 1 Last Question on Taylor Polynomials

1. ## 1 Last Question on Taylor Polynomials

I was able to understand all of the questions (after your guys' help, once again, thank you very much) up until this one which kind of reverses the question:

Suppose that f is a function such that $\displaystyle f(1) = 1, f '(1) = 2$, and $\displaystyle f ''(x) = \frac {1}{(1 + x^3)}$ for $\displaystyle x > -1$

a) Estimate $\displaystyle f(1.5)$ using a quadratic Taylor polynomial.

b) Find an upper bound on the approximation error made in part (a).

2. Originally Posted by larson
I was able to understand all of the questions (after your guys' help, once again, thank you very much) up until this one which kind of reverses the question:

Suppose that f is a function such that $\displaystyle f(1) = 1, f '(1) = 2$, and $\displaystyle f ''(x) = \frac {1}{(1 + x^3)}$ for $\displaystyle x > -1$

a) Estimate $\displaystyle f(1.5)$ using a quadratic Taylor polynomial.

b) Find an upper bound on the approximation error made in part (a).
The Taylor polynomial of degree 2 for a well-behaved function at a point is $\displaystyle f(a) + f'(a)(x-a)+(f''(a)/2!)(x-a)^2$. This means you want to find the this Taylor polynomial at $\displaystyle a=1$ and use the infromation given above.