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Details for 178_IsDecr.mw

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> restart;

> IsDecr := proc( F, a, b )

> local b2, R;

> R:=is( diff(F,x), negative ) assuming x>a, x

> if R=FAIL then
b2 := `if`(b=infinity,a+100,b);
R:=convert( map( is, [seq(eval(F,x=k), k=a..b2)], negative ), `and` );

> end if;

> return R

> end proc:

> f := arctan(x)/(1+x^2);

Maple Equation

> debug( IsDecr );

Maple Equation

> IsDecr( f, 1, infinity );

--> enter IsDecr, args = `/`(`*`(arctan(x)), `*`(`+`(1, `*`(`^`(x, 2))))), 1, infinity

Maple Equation

<-- exit IsDecr (now at top level) = false

Maple Equation

> df := simplify( diff( f, x ) );

Maple Equation

> solve( df=0, x );

Maple Equation

> allvalues( % );

Maple Equation

> plot( [f,df], x=0..5 );

Maple Plot

> ?Student[Calculus1]

> Student[Calculus1]:-CriticalPoints(f);

Maple Equation

> Student[Calculus1]:-CriticalPoints(f, x);

Maple Equation

> Student[Calculus1]:-CriticalPoints(f, x=0..1, numeric);

Maple Equation

> eval( df, x=0.765378 );

Maple Equation

> eval( df, x=0.653271 );

Maple Equation

> fsolve( df=0, x=0..10 );

Maple Equation

>

Maple Equation

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