### Related

##### define-diff-expand-float-realroots-rhs

define(B(x),expand(x^...

define(Bp(x),diff(B(x...

xx : realroots(Bp(x)=0);

Calculate

##### define-diff-expand-float-realroots

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

f(2) ;

float ( f(-1) ) ;

Calculate

##### define-diff-expand-float-realroots-rhs

define(c(x),60-3*x);

define(B(x),x^2*c(x));

define(Bp(x),diff(exp...

Calculate

##### define-diff-expand-float-realroots

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

f(2);

f(-1);

Calculate

##### define-diff-expand-float-realroots

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

f(-1);

float(f(-6));

Calculate

##### define-diff-expand-float-realroots

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

f(-1);

float(f(-6));

Calculate

##### define-diff-expand-float-realroots

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

f(-1);

float(f(-6));

Calculate

##### define-diff-expand-float-realroots

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

float (r: realroots( ...

define (fp(x), diff(f...

Calculate

##### define-diff-expand-float-realroots

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

f(-1);

float(f(-6));

Calculate

##### define-diff-expand-float-realroots-rhs

define(c(x),60-3*x);

define(B(x),expand(x^...

define(Bp(x),diff(B(x...

Calculate

### [define,diff,expand,float,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)=0));
(%o4)                       [x = 2.209753304719925]
(%i5) define ( fp (x), diff (f(x),x) );
2           3
3 x  + 1   3 (x  + x - 13)
(%o5)                 fp(x) := -------- - ---------------
3             4
5 x           5 x
(%i6) a: 1.5;
(%o6)                                 1.5
(%i7) b: 3;
(%o7)                                  3
(%i8) h: b-a;
(%o8)                                 1.5
(%i9) dq: (f(a+h)-f(a))/h;
(%o9)                          0.40493827160494
(%i10) define (z(x), expand (f(a) + dq * (x-a)));
(%o10)          z(x) := 0.40493827160494 x - 1.088888888888889
(%i11) ```
Run Example
```define(f(x),(x^3+x-13)/(5*x^3));
3
x  + x - 13
(%o1)                         f(x) := -----------
3
5 x
(%i2) f(2);
3
(%o2)                                - --
40
(%i3) f(-1);
(%o3)                                  3
(%i4) float(f(-6));
(%o4)                          0.21759259259259
(%i5) r:realroots(f(x)=0);
74147017
(%o5)                           [x = --------]
33554432
(%i6) float(r);
(%o6)                       [x = 2.209753304719925]
(%i7) define(fp(x),diff(f(x),x));
2           3
3 x  + 1   3 (x  + x - 13)
(%o7)                 fp(x) := -------- - ---------------
3             4
5 x           5 x
(%i8) fp(1.5);
(%o8)                          1.422222222222222
(%i9) a:1.5;
(%o9)                                 1.5
(%i10) b:3;
(%o10)                                 3
(%i11) h:b-a;
(%o11)                                1.5
(%i12) dq:(f(a+h)-f(a))/h;
(%o12)                         0.40493827160494
(%i13) define(z(x),expand(f(a)+dq*(x-a)));
(%o13)          z(x) := 0.40493827160494 x - 1.088888888888889
(%i14) ```
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) define ( fp (x), diff (f(x),x) );
2           3
3 x  + 1   3 (x  + x - 13)
(%o5)                 fp(x) := -------- - ---------------
3             4
5 x           5 x
(%i6) a: 0.5;
(%o6)                                 0.5
(%i7) b: 2.5;
(%o7)                                 2.5
(%i8) h: b-a;
(%o8)                                 2.0
(%i9) fp (1.5);
(%o9)                          1.422222222222222
(%i10) define (z(x), expand (f(a) + fp * (x-a)));
(%o10)                   z(x) := fp x - 0.5 fp - 19.8
(%i11) ```

### Related Help

Help for Define

Help for Diff

Help for Expand

Help for Float

Help for Realroots