3.          Given f(x) = `^`(x, sin(x)); -1 

restart;  

 

with(Student[Calculus1]); -1 

 

f := proc (x) options operator, arrow, function_assign; `^`(x, sin(x)) end proc;  

f := proc (x) options operator, arrow; `^`(x, sin(x)) end proc; (7.3.1)
 

plot(f(x), x = 0 .. 10);  

Plot_2d
 

ExtremePoints(f(x), 0 .. 10);  

 

Warning, some extreme points are returned as numeric approximations
[0, .3522153993, 2.127615825, 4.842558340, 7.914977694, 10]; (7.3.2)
 

 

List1; (7.3.3)
 

List1 := [0, .3522153993, 2.127615825, 4.842558340, 7.914977694, 10];  

List1; (7.3.4)
 

map(f, List1);  

[1, .6976840988, 1.898286456, .2092767216, 7.884585439, `^`(10, sin(10))]; (7.3.5)
 

 

InflectionPoints(f(x), x = 0 .. 10, numeric);  

[1.395288666, 2.916095860, 7.258616748, 8.576145756]; (7.3.6)
 

 

List2; (7.3.7)
 

map(f, List2);  

[1.388167079, 1.270355626, 5.161057841, 5.015577534]; (7.3.8)