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z4VN-c;0Rl_fK8i1PTi?x>-X_BFZVoYVHYOHsW)1;jzW=vG?|(fG#LS%B#Q%NU6HIWz1%aZ3%;L;DOmiPc z|I>>h9111t8=LFUAJEi;@`K!iIJQJH>!8ml17$}B~P8(_@BoIy(~s8&{aWQ+}RmOlW 0 \exists \delta > 0 | \forall h > 0, \text{if } 0 < h < \delta \Rightarrow$$ -$$\left| \frac{f(x + h) - f(x - h)}{2h} - f'(x)\right| = \left|f'(x) - \frac{f(x + h) - f(x - h)}{2h}\right| < \epsilon$$ +$$\frac{f(x + h) - f(x - h)}{2h} \geq +\frac{1}{2h} \cdot +\left(2hf'(x) + \frac{2h^3f'''(x)}{6} \right) = +f'(x) + \frac{h^2f'''(x)}{6} +$$ -I GIVE UP :( +So: + +$$ \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} + \Rightarrow +C = \frac{f'''(x)}{6}$$ \section*{Question 4} \subsection*{Point a)}