I have a function, which is $f(x) = e^{1/x}$. I want to calculate the error bound for the Trapezoid Rule
, which formula is:
$|E|\leq K\frac{(a-b)^3}{12\cdot n^2}$
where $|f''(x)|\leq K$. What's the value of $K$ for the above function? If I calculated $f''(x)$ correctly, it should be: $f"(x) = \frac{e^{1/x}}{x^3}\left(\frac 1x + 2\right).$
Please correct me if I'm wrong. The boundaries are $[1, 2]$.