VIPSolutionsFind dy forthe given values of x and Ax. y=2¢- Bx x= ~2and Ax=02 a=] (Round to the nearest tenth as needed.)
Question:
Find dy forthe given values of x and Ax.
y=2¢- Bx x= ~2and Ax=02
a=]
(Round to the nearest tenth as needed.)
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Asked by: Test User 100045
Created at: 2025-05-07 22:33:19
Asked by: Test User 100045
Created at: 2025-05-07 22:33:19
Final Answer:
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Given:
\( y = 2x^3 - 8x \)
\( x = -2 \)
\( \Delta x = 0.2 \)
To find \( dy \):
1. **Find \( \frac{dy}{dx} \) (the derivative of \( y \) with respect to \( x \)):**
\[
\frac{dy}{dx} = \frac{d}{dx}(2x^3 - 8x) = 6x^2 - 8
\]
2. **Evaluate \( \frac{dy}{dx} \) at \( x = -2 \):**
\[
\frac{dy}{dx}\Bigg|_{x=-2} = 6(-2)^2 - 8 = 6(4) - 8 = 24 - 8 = 16
\]
3. **Use the differential formula:**
\[
dy = \frac{dy}{dx} \cdot \Delta x = 16 \cdot 0.2 = 3.2
\]
**Final answer:**
\[
\boxed{3.2}
\]
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