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 $y = f(x)$ at the points $(-4, -1)$ and $(-1, -5)$. ‖ ‖ step 2 ⋮ The slope of the tangent line at a point on a curve represents the derivative of the function at that point. ‖ ‖ step 3 ⋮ Observing the graph, the tangent line at $(-4, -1)$ appears to be less steep (closer to horizontal) compared to the tangent line at $(-1, -5)$, which is steeper (more vertical). ‖ ‖ step 4 ⋮ Therefore, $f'(-4)$ is less than $f'(-1)$. ‖ ***A*** ∻Key Concept∻ ⚹Comparing derivatives⚹ ∻Explanation∻ ⚹The derivative at a point on a curve represents the slope of the tangent line at that point. By comparing the steepness of the tangent lines at the given points, we can determine the relative values of the derivatives.⚹◊What is the significance of comparing $f'(-4)$ and $f'(-1)$ based on the given graph of the function $y = f(x)$?⍭ Generate me a similar question◊

Sia