elena is making an open - top box by cutting squares out of the corners of a piece of paper that is 11…

elena is making an open - top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides.\nif the side lengths of her square cutouts are x inches, then the volume of the box is given by ( v(x)=x(11 - 2x)(17 - 2x) ).\nelena graphs the volume of the box along with the function ( b(x)=140 ).\nwhat is the maximum volume of this box?\nfor what x values is this function decreasing? <x<

elena is making an open - top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides.\nif the side lengths of her square cutouts are x inches, then the volume of the box is given by ( v(x)=x(11 - 2x)(17 - 2x) ).\nelena graphs the volume of the box along with the function ( b(x)=140 ).\nwhat is the maximum volume of this box?\nfor what x values is this function decreasing? <x<

Answer

Explanation:

Step1: Identify maximum volume from graph

The maximum value of the (y = V(x)) graph (which represents volume) is (180) (from the (y -)axis label of the peak).

Step2: Determine decreasing interval

A function (y = f(x)) is decreasing when the slope of the tangent line is negative. Looking at the (y=V(x)) graph, it is decreasing for (2 < x < 8) (by observing the part of the graph where as (x) increases, (y) decreases).

Answer:

The maximum volume of the box is (180) cubic inches. The function (y = V(x)) is decreasing for (2<x < 8).