This isnt strictly in the form required in denition

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 − 2x) = 4x3 − 44x2 + 120x To find a suitable applied domain, we note that to make a box at all we need x > 0. Also the shorter of the two dimensions of the cardboard is 10 inches, and since we are removing 2x inches from this dimension, we also require 10 − 2x > 0 or x < 5. Hence, our applied domain is 0 < x < 5. 2. Using a graphing calculator, we see the graph of y = V (x) has a relative maximum. For 0 < x < 5, this is also the absolute maximum. Using the ‘Maximum’ feature of the calculator, we get x ≈ 1.81, y ≈ 96.77. The height, x ≈ 1.81 inches, the width, 10 − 2x ≈ 6.38 inches, and the depth 12 − 2x ≈ 8.38 inches. The y -coordinate is the maximum volume, which is approximately 96.77 cubic inches (also written in3 ). 4 this is a dangerous word... There’s no harm in taking an extra step here and making sure this makes sense. If we chopped out a 1 inch square from each side, then the width would be 8 inches, so chopping out x inches would leave 10 − 2x inches. 6 When we write V (x), it is in the context of function notation, not the volume V times the quant...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online