ma142ahw6solns

ma142ahw6solns - x ² x 2 2 , µ x, 0, 20 ! , PlotRange #...

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which is approximately 1.44467
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Mathematica Plots x^ ± 1 ² x ³ and its first and second derivative Plot ´ x^ ± 1 ² x ³ , µ x, 0, 100 20 40 60 80 100 1.0 1.1 1.2 1.3 1.4 E^ ± 1 ² E ³·· N 1.44467 In[1]:= f ¸ x_ ¹ ! x^ ± 1 ² x ³ Out[1]= x 1 x In[13]:= g ¸ x_ ¹ ! D º x 1 x ,x » Out[13]= x 1 x 1 x 2 " Log ± x ² x 2 Plot º x 1 x 1 x 2 " Log ¸ x ¹ x 2 , µ x, 0, 100 ! , PlotRange # Full » 20 40 60 80 100 0.5 1.0 1.5 In[14]:= E 1 E 1 E 2 " Log ´ E E 2 Out[14]= 0 The first derivative is 0 at E.
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h ± x ² ! D ³ x 1 x 1 x 2 " Log ± x ² x 2 ,x ´ x 1 x " 3 x 3 $ 2 Log ± x ² x 3 $ x 1 x 1 x 2 " Log ± x ² x 2 2 Plot ³ x 1 x " 3 x 3 $ 2 Log ± x ² x 3 $ x 1 x 1 x 2 " Log ±
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Unformatted text preview: x ² x 2 2 , µ x, 0, 20 ! , PlotRange # Full ´ 5 10 15 20 " 2 2 4 6 8 In[16]:= E 1 E " 3 E 3 $ 2 Log ¶ E · E 3 $ E 1 E 1 E 2 " Log ¶ E · E 2 2 Out[16]= "± " 3 $ 1 ± In[17]:= % ¸¸ N Out[17]= " 0.0719258 The second derivative is negative at E and thus we get a local max. 2 hw6 problem4b.nb...
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This note was uploaded on 10/17/2010 for the course MAT Math10C taught by Professor Operadragos during the Spring '09 term at UCSD.

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ma142ahw6solns - x ² x 2 2 , µ x, 0, 20 ! , PlotRange #...

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