= Solution
For $n$ equal strips and a uniform bound $|f''(x)|\leq M$ on $[a,b]$, the <composite trapezoidal error bound> is
$$
|I-T_n|\leq\frac{(b-a)^3M}{12n^2}.
$$
On $[1,25]$, part (b) gives $M=1/2$: $f''$ is positive and decreases from $1/2$ after $x=1$. Hence
$$
|I-T_n|\leq\frac{24^3}{24n^2}=\frac{576}{n^2}.
$$
To certify error at most $10^{-4}$, choose \b[$n\geq2400$]; equality gives exactly $10^{-4}$ in this bound. This is a sufficient certificate, not a claim that every smaller $n$ fails in actual numerical error.
Strictly, the maximum specified over the open interval $(1,25)$ is not attained; its <supremum> is $1/2$. Using the maximum on the closed interval, or simply the uniform bound $M=1/2$, gives the valid error estimate above.
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