http://openstudy.com/study#/updates/5477a78de4b0de37d41bc8a7

In[7]:= Clear@"Global`*"D; $Line = 0;

Make the polynomial a temporary Mathematica function.

In[1]:= g@x_D := x3

+ 5 x2

- 17 x - 21

In[2]:= Plot@g@xD, 8x, -9, 7<D

Out[2]=

-5 5

-200

-100

100

200

Set the partial derivative of g(x) to zero and solve the result for x.

In[3]:= ¶x Hg@xDL � 0 �� Solve �� Flatten

Out[3]= :x ®

1

3

I-5 - 2 19 M, x ®

1

3

I-5 + 2 19 M>

Ask Mathematica to convert the above to their numeric values.

% refers to the last Mathematica calculation result, Out[3] in this case.

In[4]:= % �� N

Out[4]= 8x ® -4.5726, x ® 1.23927<

Plug in the first symbolic solution for x from Out[3], into g(x), and then simplify the

result. ® expressions are replacement rules and /. is the replacement operator.

In[5]:= g@x �. %3@@1DD

D �� Simplify

Out[5]=

16

27

I28 + 19 19 M

The above calculated to 50 digits. Mathematica is capable of unlimited precision

arithematic.

In[6]:= N@%, 50D

Out[6]= 65.670565882828324440001574929382339273246266417432