I need to find $k$ for the trapezoidal rule.
$\exp\left(\dfrac{x^2}{2}\right)$ is my function on the interval $[0,2]$
The second derivative would be $(x^2+1)\exp\left(\dfrac{x^2}{2}\right)$. In my calculator its saying the maximum is $8090$. But I don't think this is right.
Any help?
It appears you are trying to maximize $(x^2 + 1) \exp(x^2/2)$ on the interval $[0,2]$. Is that right?
If so, then your function is strictly increasing for $x \geq 0$. Thus your function is maximized at the right endpoint of its interval, and the max is $5 e^2$. This is not so big.