I have an equation, $e^x$, based at 0 (b=0).
I am supposed to us the Tangent Line Error Bound to bound the error $|f(x)-T1(x)|$ on the interval I=[-1,1].
(Aside: I have already computed the first Taylor Polynomial $T1(x)$ for $e^x$ at b=0 to be $1+x$)
To find the error, I have done the following:
- Found the second derivative of $f(x)$ to be $f''(x)=e^x$.
- Found $M$, the maximum of $f''(x)$, to be $e^1$ on the interval [-1,1].
Now, the notes I have on finding the error are slightly confusing in that they indicate the method to find the error is one of the following:
- $\frac{M}{(n+1)!} | x - b |^{n+1}$
- $\frac{M}{(n+1)!} | d - b |^{n+1}$
However, using either of these in the homework submission website indicate wrong answers. What am I doing wrong?