2. Given f(x) = `+`(exp(sin(x)), `*`(`/`(1, 2), `*`(x))); limited to the interval   

 

restart;  

f := proc (x) options operator, arrow, function_assign; `+`(exp(sin(x)), `*`(`/`(1, 2), `*`(x))) end proc;  

f := proc (x) options operator, arrow; `+`(exp(sin(x)), `*`(`/`(1, 2), `*`(x))) end proc; (7.2.1)
 

with(Student[Calculus1]); -1 

FunctionChart(f(x), x = -10 .. 10);  

Plot_2d
 

 

CurveAnalysisTutor(f(x), x = -10 .. 10);  

Plot_2d 

 

 

diff(f(x), x);  

`+`(`*`(cos(x), `*`(exp(sin(x)))), `/`(1, 2)); (7.2.2)
 

 

fp(x); (7.2.3)
 

diff(fp(x), x);  

`+`(`-`(`*`(sin(x), `*`(exp(sin(x))))), `*`(`^`(cos(x), 2), `*`(exp(sin(x))))); (7.2.4)
 

 

fpp(x); (7.2.5)
 

with(plots); -1 

 

inequal([`>`(fp(x), 0), `>`(fpp(x), 0)], x = -10 .. 10, y = -5 .. 5);  

Plot_2d