unit raboty;

interface
  uses sysutils, math, Funcii;

  type
    tArrFX = array of extended;
  procedure FotX(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  procedure Integtal(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  procedure dF_dX(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  procedure d2F_dX2(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  procedure Korni(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  procedure Extremumy(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);

implementation

  procedure FotX(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  var h,x: extended;
  begin
    h:=(b-a)/N;
    x:=a;
    while x <= b do
    begin
      setlength(ArrFX, length(ArrFX)+1);
      ArrFX[high(ArrFX)]:=f1(x);
      x:=x+h;
    end;
  end;

  procedure Integtal(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  var h,x,s: extended;
  begin
    h:=(b-a)/N;
    x:=a;
    s:=0;
    while x <= b do
    begin
      s:=s+(f1(x)+f1(x+h))*h/2;
      setlength(ArrFX, length(ArrFX)+1);
      ArrFX[high(ArrFX)]:=s;
      x:=x+h;
    end;
  end;
  
  procedure dF_dX(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  var h,x: extended;
  begin
    h:=(b-a)/N;
    x:=a;
    while x <= b do
    begin
      setlength(ArrFX, length(ArrFX)+1);
      ArrFX[high(ArrFX)]:=(f1(x+h)-f1(x))/h;
      x:=x+h;
    end;
  end;

  procedure d2F_dX2(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  var h,x: extended;
  begin
    h:=(b-a)/N;
    x:=a;
    while x <= b do
    begin
      setlength(ArrFX, length(ArrFX)+1);
      ArrFX[high(ArrFX)]:=((f1(x+2*h)-f1(x+h))/h
      -(f1(x+h)-f1(x))/h)/h;
      x:=x+h;
    end;
  end;

  procedure Korni(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  var h,x: extended;
  begin
    h:=(b-a)/N;
    x:=a;
    while x < b do
    begin
     if f1(x)*f1(x+h)<0 then begin
      setlength(ArrFX, length(ArrFX)+1);
      ArrFX[high(ArrFX)]:=x;
     end;
      x:=x+h;
    end;
  end;

  procedure Extremumy(f1:tFuncX; a,b:extended; N:integer; out ArrFX:tArrFX);
  var h,x: extended;
  begin
    h:=(b-a)/N;
    x:=a;
    while x < b do
    begin
     if ((f1(x)<f1(x+h)) and (f1(x+2*h)<f1(x+h)) )
     or ((f1(x)>f1(x+h)) and (f1(x+2*h)>f1(x+h))) then begin
      setlength(ArrFX, length(ArrFX)+1);
      ArrFX[high(ArrFX)]:=x+h;
     end;
      x:=x+h;
    end;
  end;


end.