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

Question

Compare.
$$
f^{\prime}(-4) \text { _-- } f^{\prime}(-1)
$$

Choose 1 answer:
(A) $<$
(B) $>$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To compare $f'(-4)$ and $f'(-1)$, we need to analyze the slopes of the tangent lines to the curve at the points $(-4, -1)$ and $(-1, -5)$. ‖ ‖ 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.⚹◊What is the relationship between $f'(-4)$ and $f'(-1)$ for the given function $y = f(x)$?⍭ Generate me a similar question◊

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