The problem starts with the integral of 1/(1+x^4) on the interval of (1,2). I'm trying to find the upper bound of error using the trapezoidal rule. The formula is - (b-a)^2/12n^2 x f"(c). My problem is with finding |f"(c)|.
f"(c) = 4c^2(5c^4-3)/(1+c^4). This is the second derivitive. My solution manual uses c=2 for the upper bound and so plugs it in to f"(c) except in the denominator of 1+c^4. It uses 1. So it's 4(2)^2[5(2)^2-3]/1+(1)^4. Why is that? I know this can look complicated and if you would like me to clarify any part of this question let me know. I would highly appreciate if you would give your time and effort in helping me.
f"(c) = 4c^2(5c^4-3)/(1+c^4). This is the second derivitive. My solution manual uses c=2 for the upper bound and so plugs it in to f"(c) except in the denominator of 1+c^4. It uses 1. So it's 4(2)^2[5(2)^2-3]/1+(1)^4. Why is that? I know this can look complicated and if you would like me to clarify any part of this question let me know. I would highly appreciate if you would give your time and effort in helping me.