Byrd Gibson
04/29/2023 · Elementary School
Sketch the graph of a function that has the properties described below. \( (-3,-1),(-1,-4) \), and \( (1,-7) \) are on the graph; \( f^{\prime}(-3)=0 \) and \( f^{\prime}(1)=0 ; f^{\prime \prime}(x)<0 \) for \( x<-1, f^{\prime \prime}(-1)=0, f^{\prime \prime}(x)>0 \) for \( x>-1 \).
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The graph has points \((-3,-1)\), \((-1,-4)\), and \((1,-7)\). It has a local maximum at \((-3,-1)\), a local minimum at \((1,-7)\), and is concave down for \(x < -1\) and concave up for \(x > -1\).
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