4.6 Connecting Graphs Of F, F', F''ap Calculus



Answer

4.6 Connecting Graphs Of F F' F'ap Calculus 2nd Edition

$limlimits_{h to 0}frac{f(x+h)-f(x-h)}{2h} = f'(x)$ The diagram shows that the slope of the line connecting the points $(x-h, f(x-h))$ and $(x+h, f(x+h))$ approaches the slope of the graph at $x$ as $hto 0$
4.6 Connecting Graphs Of F, F4.6 Connecting Graphs Of F, F

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4.6 Connecting Graphs Of F F' F'ap Calculus Calculator

4.6 connecting graphs of f f

Work Step by Step

$limlimits_{h to 0}frac{f(x+h)-f(x-h)}{2h} = frac{0}{0}$ We can apply L'Hospital's Rule. $limlimits_{h to 0}frac{f'(x+h)-(-1)f'(x-h)}{2} = frac{2f'(x)}{2} = f'(x)$ The diagram shows that the slope of the line connecting the points $(x-h, f(x-h))$ and $(x+h, f(x+h))$ approaches the slope of the graph at $x$ as $hto 0$