Thomas Calculus 13th [Solutions]

232 Chapter 4 Applications of Derivatives
89. Maximum value is 5 on the interval [3, );
minimum value is 5 on the interval ( , 2].
90. Minimum value is 4 on the interval [ 1, 3]
91-98. Example CAS commands:
Maple:
with(student):
f : x - x^4-8*x^2 4*x 2;
domain : x -20/25..64/25;
plot( f(x), domain, color black, title "Section 4.1 #91(a)" );
Df : D(f );
plot( Df(x), domain, color black, title "Section 4.1 #91(b)" )
StatPt : fsolve( Df(x) 0, domain )
SingPt : NULL;
EndPt : op(rhs(domain));
Pts : evalf ([EndPt,StatPt,SingPt]);
Values : [seq( f(x), x Pts )];
Maximum value is 2.7608 and occurs at x 2.56 (right endpoint).
Minimum value is -6.2680 and occurs at x 1.86081 (singular point).
Mathematica: (functions may vary) (see Section 2.5 re. RealsOnly ):