### Related

##### define-expand-float-plot2d-realroots

define(f(x),(x^3+x-13...

f(-1);

float(f(-6));

Calculate

##### define-expand-float-plot2d-realroots

define(r(x), (x^3-5*x...

a: .75;

b: 3.25;

Calculate

##### define-expand-float-plot2d-realroots

define(f(x), (x^3+x-1...

f(-1);

float(f(-6));

Calculate

##### define-expand-float-plot2d-realroots

define(f(x), (x^3 + 2...

a: 4.5;

b: 6;

Calculate

##### define-expand-float-plot2d-realroots

define(f(x), x^3 + 3*...

define(g(x), x^3 + 13);

define(r(x), f(x)/g(x));

Calculate

##### define-expand-float-plot2d-realroots

define (r(x), (x^3-5*...

a : 0.75;

b: 3.25;

Calculate

##### define-expand-float-plot2d-realroots

define (r(x), (x^3-5*...

a : 0.75;

b: 3.25;

Calculate

##### define-expand-float-plot2d-realroots

define(f(x),(x^3+x-13...

f(-1);

float(f(-6));

Calculate

##### define-expand-float-plot2d-realroots

define(f(x), (x^3+x-1...

f(-1);

float(f(-6));

Calculate

##### define-expand-float-plot2d-realroots

define(f(x), (x^3 + 2...

a: 4.5;

b: 6;

Calculate

### [define,expand,float,plot2d,realroots]

Run Example
```(%i1)define(f(x), (x^3+x-13)/(5*x^3));
3
x  + x - 13
(%o1)                         f(x) := -----------
3
5 x
(%i2) f(-1);
(%o2)                                  3
(%i3) float(f(-6));
(%o3)                          0.21759259259259
(%i4) float(realroots(f(x)));
(%o4)                       [x = 2.209753304719925]
(%i5) a:1.5;
(%o5)                                 1.5
(%i6) b:3;
(%o6)                                  3
(%i7) h:(b-a);
(%o7)                                 1.5
(%i8) dq:(f(a+h)-f(a))/h;
(%o8)                          0.40493827160494
(%i9) define(z(x),expand(f(a)+dq*(x-a)));
(%o9)           z(x) := 0.40493827160494 x - 1.088888888888889
(%i10) plot2d(f(x),[x,1,4],[y,-1,0.5]);
plot```
Run Example
```define(f(x), x^3 + 3*x^2 -14*x + 5);
3      2
(%o1)                    f(x) := x  + 3 x  - 14 x + 5
(%i2) define(g(x), x^3 + 13);
3
(%o2)                           g(x) := x  + 13
(%i3) define(r(x), f(x)/g(x));
3      2
x  + 3 x  - 14 x + 5
(%o3)                    r(x) := --------------------
3
x  + 13
(%i4) plot2d([r(x)],[x,-10,10],[y,-5,5]);
plotfloat(realroots(r(x)=0));
(%o5) [x = - 5.639635533094406, x = 0.39497354626656, x = 2.244661957025528]
(%i6) float(realroots(f(x)=0));
(%o6) [x = - 5.639635533094406, x = 0.39497354626656, x = 2.244661957025528]
(%i7) a: -1;
(%o7)                                 - 1
(%i8) b: 5;
(%o8)                                  5
(%i9) h: b-a;
(%o9)                                  6
(%i10) dq: (r(a+h)-r(a))/h;
71
(%o10)                               - ---
552
(%i11) define(s(x), r(a)+dq*(x-a));
7   71 (x + 1)
(%o11)                      s(x) := - - ----------
4      552
(%i12) expand(s(x));
895   71 x
(%o12)                            --- - ----
552   552
(%i13) plot2d([r(x),s(x)],[x,-10,10],[y,-5,5]);
plot```
Run Example
```define(f(x),(x^3+x-13)/(5*x^3));
3
x  + x - 13
(%o1)                         f(x) := -----------
3
5 x
(%i2) f(-1);
(%o2)                                  3
(%i3) float(f(-6));
(%o3)                          0.21759259259259
(%i4) float(realroots(f(x)=0));
(%o4)                       [x = 2.209753304719925]
(%i5) a:1.5;
(%o5)                                 1.5
(%i6) b: 3;
(%o6)                                  3
(%i7) h: b-a;
(%o7)                                 1.5
(%i8) dq:(f(a+h)-f(a))/h;
(%o8)                          0.40493827160494
(%i9) define(z(x),expand(f(a)+dq*(x-a)));
(%o9)           z(x) := 0.40493827160494 x - 1.088888888888889
(%i10) plot2d([f(x),z(x)],[x,1,4],[y,-1,.5]);
plot```

### Related Help

Help for Define

Help for Expand

Help for Float

Help for Plot2d

Help for Realroots