Function $h$ is graphed. Select all the intervals where $h^{\prime}(x)0$ and $h^{\prime \prime}(x)

Q: Function $h$ is graphed. Select all the intervals where $h^{\prime}(x)>0$ and $h^{\prime \prime}(x)<0$. Choose all answers that apply: A $-4.5<x<-3$ B $-3<x<-1$ c) $-1<x<1$ D None of the above

∻Solution by Steps∻ ‖ step 1 ⋮ To determine where $h'(x) > 0$ and $h''(x) 0$ indicates that the function $h(x)$ is increasing. This occurs where the slope of the tangent to the curve is positive. ‖ ‖ step 3 ⋮ $h''(x) 0$ and $h''(x)

Question

Function $h$ is graphed.

Select all the intervals where $h^{\prime}(x)>0$ and $h^{\prime \prime}(x)<0$.
Choose all answers that apply:

A $-4.5<x<-3$

B $-3<x<-1$
c) $-1<x<1$

D None of the above

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine where $h'(x) > 0$ and $h''(x) < 0$, we need to analyze the graph of $h(x)$. ‖ ‖ step 2 ⋮ $h'(x) > 0$ indicates that the function $h(x)$ is increasing. This occurs where the slope of the tangent to the curve is positive. ‖ ‖ step 3 ⋮ $h''(x) < 0$ indicates that the function $h(x)$ is concave down. This occurs where the slope of the tangent to the curve is decreasing. ‖ ‖ step 4 ⋮ From the graph, we observe that $h(x)$ is increasing and concave down in the interval $-3 < x < -1$. ‖ ***B*** ∻Key Concept∻ ⚹Intervals of Increase and Concavity⚹ ∻Explanation∻ ⚹To find where $h'(x) > 0$ and $h''(x) < 0$, we look for intervals where the function is increasing and concave down.⚹◊What is the relationship between the behavior of the function $h(x)$ and the signs of its first and second derivatives in the given intervals?⍭ Generate me a similar question◊

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