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Numerade Educator

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Problem 20 Medium Difficulty

Compute $ \Delta y $ and $ dy $ for the given values of $ x $ and $ dx = \Delta x. $ Then sketch a diagram like Figure 5 showing the line segments with lengths $ dx, dy, $ and $ \Delta y. $
$ y = x - x^3, x = 0, \Delta x = -0.3 $

Answer

$\Delta y=-0.273, d y=-0.3$

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Video Transcript

first off for the derivative? No, the derivative of X minus X cubed is gonna be one minus three acts square times d x. Now we know that Delta X or the changing Exes night of 0.3, which is DX therefore f of zero plus negative 0.3 minus off of zero. We have one times negative 0.3, which is negative. Zero point three. Then we know that Delta Why is negative? 0.273 We know this area over here is Do you? Why on this area over here is ddx.