The second, ”( ), and fourth, ””( ), derivatives of a function ( ) are plotted in Figure 6.17. This question concerns evaluating (a) How large must  be to guarantee the error using the composite...

The second,
”(), and fourth,
””(), derivatives of a function
() are plotted in Figure 6.17. This question concerns evaluating

(a) How large must
 be to guarantee the error using the composite trapezoidal rule is less than 10⁻⁸?

(b) How large must
 be to guarantee the error using the composite Simpson rule is less than 10⁻⁸?