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;
 

Typesetting:-mprintslash([f := proc (x) options operator, arrow, function_assign; `+`(exp(sin(x)), `*`(`/`(1, 2), `*`(x))) end proc], [proc (x) options operator, arrow, function_assign; `+`(exp(sin(x)... (7.2.1)
 

> with(Student[Calculus1]); -1
 

> FunctionChart(f(x), x = -10 .. 10);
 

Plot_2d
 

>
 

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

Plot_2d
 

> `and`(`*`(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(`*`(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(iii, Eyeball), the, true), `*`(graph)), Estimate), the, true), `*`(int...
 

>
 

>
 

> diff(f(x), x);
 

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

> fp := proc (x) options operator, arrow, function_assign; `+`(`*`(cos(x), `*`(exp(sin(x)))), `/`(1, 2)) end proc; -1; 'fp(x)'
 

fp(x) (7.2.3)
 

> diff(fp(x), x);
 

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

> fpp := proc (x) options operator, arrow, function_assign; `+`(`-`(`*`(sin(x), `*`(exp(sin(x))))), `*`(`^`(cos(x), 2), `*`(exp(sin(x))))) end proc; -1; 'fpp(x)'
 

fpp(x) (7.2.5)
 

> with(plots); -1
 

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

Plot_2d
 

>
 

>