## anonymous 4 years ago Let y =(root3(x**5)). At x = 64 the slope of the curve = [exact] At x = 64 the slope of the curve = [approximate]

1. Rogue

$y = \sqrt[3]{x^5} = x^{\frac{5}{3}}$$y' = \frac {d}{dx} x^{\frac{5}{3}} = \frac{5}{3} x^{\frac{2}{3}}$

2. Rogue

$y' (64) = (\frac {5}{3}) 64^{\frac{2}{3}} = \frac {5}{3} *16 = \frac {80}{3}$

3. Rogue

If you need an approximate, you can take the slop of a secant line near the point (64, 1024) $m \approx \frac {y(65)-y(63)}{65-63}\approx26.666425$ This approximation is pretty close to the exact of 80/3.