all done except 3b

midterm/midterm.tex

@@ -74,7 +74,7 @@ $$f(x+h) \geq f(x) + \frac{f'(x)}{1}\cdot h + \frac{f''(x)}{2}\cdot h^2 +
 \frac{f'''(x)}{6}\cdot h^3$$
 
   $$f(x-h) \geq f(x) - \frac{f'(x)}{1}\cdot h + \frac{f''(x)}{2}\cdot h^2 -
-\frac{f'''(x)}{6}\cdot h^3 $$ 
+\frac{f'''(x)}{6}\cdot h^3$$ 
  
 Then, we can derive that:
 
@@ -87,7 +87,9 @@ $$
 So:
 
 $$ \left|f'(x) - \frac{f(x + h) - f(x - h)}{2h}\right| \leq \left|f'(x) - \left(f'(x) + \frac{h^2f'''(x)}{6}\right)
-\right| = \frac{h^2|f'''(x)|}{6}$$
+\right| = \frac{h^2|f'''(x)|}{6}
+ \Rightarrow
+C = \frac{f'''(x)}{6}$$
 
 \section*{Question 4}
 \subsection*{Point a)}