VIPSolutionsFind dy for the given values of x and Ax. y=23-8xx=-2and Ax=03 i jie ‘ oT] (Round to the nearest tenth as needed.)
Question:
Find dy for the given values of x and Ax.
y=23-8xx=-2and Ax=03
i jie ‘
oT]
(Round to the nearest tenth as needed.)
This is AI generated Response.
Asked by: Test User 100045
Created at: 2025-05-07 22:23:46
Asked by: Test User 100045
Created at: 2025-05-07 22:23:46
Final Answer:
Rendered
Raw Text
Did you like this answer?
Let's solve the problem step by step:
Given:
- \( y = 2x^3 - 8x \)
- \( x = -2 \)
- \( \Delta x = 0.3 \)
We need to find \( dy \).
### Step 1: Find \( \frac{dy}{dx} \)
\[
\frac{dy}{dx} = \frac{d}{dx} (2x^3 - 8x) = 6x^2 - 8
\]
### Step 2: Plug in \( x = -2 \) into the derivative:
\[
\frac{dy}{dx}\Bigg|_{x=-2} = 6(-2)^2 - 8 = 6 \cdot 4 - 8 = 24 - 8 = 16
\]
### Step 3: Use the differential \( dy = \frac{dy}{dx} \Delta x \)
\[
dy = 16 \times 0.3 = 4.8
\]
**Final Answer:**
\[
\boxed{4.8}
\]
(Rounded to the nearest tenth as needed.)
📢 Instructions:
- Ask anything relatd to above question only.
- For new Question goto :