Chapter 3 - Section 3.10 - Linear Approximations and Differentials. - 3.10 Exercises - Page 259: 24

$\Delta x = dx = -0.3$ $\Delta y = -0.273$ $dy = -0.3$ We can see a sketch below.

$y = x-x^3$ $\Delta x = dx = -0.3$ When $x = 0$, then $y = (0)-(0)^3 = 0$ When $x = -0.3$, then $y = (-0.3)-(-0.3)^3 = -0.273$ $\Delta y = -0.273-(0) = -0.273$ We can find the value of $dy$: $\frac{dy}{dx} = 1-3x^2$ $dy = (1-3x^2)~dx$ $dy = [1-3(0)^2]~(-0.3)$ $dy = -0.3$ We can see a sketch below.