### Related

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

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

r: float(realroots (f...

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

Calculate

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

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

f(-1);

float (f(-6));

Calculate

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

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

f(2);

f(-1);

Calculate

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

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

f(2) ;

float ( f(-1) ) ;

Calculate

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

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

r: float(realroots (f...

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

Calculate

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

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

f(-1);

float (f(-6));

Calculate

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

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

f(-1);

float (f(-6));

Calculate

##### define-diff-expand-find_root-float-realroots-solve

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

f(-1);

float (f(-6));

Calculate

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

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

f(-1);

float (f(-6));

Calculate

##### define-diff-expand-find_root-float-realroots-solve

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

f(-1);

float (f(-6));

Calculate

### [define,diff,expand,find_root,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(2);
3
(%o2)                                - --
40
(%i3) f(-1);
(%o3)                                  3
(%i4) float(f(-6));
(%o4)                          0.21759259259259
(%i5) r: float(realroots( f(x)=0));
(%o5)                       [x = 2.209753304719925]
(%i6) define(fp(x), diff(f(x),x));
2           3
3 x  + 1   3 (x  + x - 13)
(%o6)                 fp(x) := -------- - ---------------
3             4
5 x           5 x
(%i7) s: float(find_root(f(x)= fp(x), x, 2,0));
3                         2
0.2 (x  + x - 13.0)   0.2 (3.0 x  + 1.0)
(%o7) find_root(------------------- = ------------------
3                     3
x                     x
3
0.6 (x  + x - 13.0)
- -------------------, x, 0.0, 2.0)
4
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(float(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) float (find_root (f(x)=fp (x), x, 0, 10));
3                         2
0.2 (x  + x - 13.0)   0.2 (3.0 x  + 1.0)
(%o6) find_root(------------------- = ------------------
3                     3
x                     x
3
0.6 (x  + x - 13.0)
- -------------------, x, 0.0, 10.0)
4
x
(%i7) a: 1.5;
(%o7)                                 1.5
(%i8) b: 3;
(%o8)                                  3
(%i9) h: b-a;
(%o9)                                 1.5
(%i10) dq: (f(a+h)-f(a))/h;
(%o10)                         0.40493827160494
(%i11) define (z(x), expand (f(a) + dq * (x-a)));
(%o11)          z(x) := 0.40493827160494 x - 1.088888888888889
(%i12) ```
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) float (find_root (f(x)=fp , x, 0, 10));
3
0.2 (x  + x - 13.0)
(%o6)          find_root(------------------- = fp, x, 0.0, 10.0)
3
x
(%i7) a: 1.5;
(%o7)                                 1.5
(%i8) b: 3;
(%o8)                                  3
(%i9) h: b-a;
(%o9)                                 1.5
(%i10) dq: (f(a+h)-f(a))/h;
(%o10)                         0.40493827160494
(%i11) define (z(x), expand (f(a) + dq * (x-a)));
(%o11)          z(x) := 0.40493827160494 x - 1.088888888888889
(%i12) ```

### Related Help

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Help for Expand

Help for Find_root

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