Question

Math

Posted 3 months ago

```
Compare.
f^{\prime}(-4) \text { _-- } f^{\prime}(-1)
Choose 1 answer:
(A) $<$
(B) $>$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

At $x = -4$, the curve is decreasing, indicating that $f'(-4)$ is negative

step 3

At $x = -1$, the curve is also decreasing, but the slope appears to be steeper than at $x = -4$, indicating that $f'(-1)$ is more negative than $f'(-4)$

step 4

Since $f'(-1)$ is more negative than $f'(-4)$, we have $f'(-4) > f'(-1)$

B

Key Concept

Comparison of derivatives

Explanation

To compare the derivatives at two points on a curve, we analyze the slopes of the tangent lines at those points. A steeper negative slope indicates a more negative derivative.

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