Question

Function a(e) represents the surface area of a cube in terms of its edge length, e, and the difference quotient is 12e 6h. what is the average rate of change in surface area of a cube as the edge length increases from 3 inches to 5 inches?

Answer 1

48 square inches per inch is the average rate of change in surface area.

What is an area in math?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

The surface area of a cube of side length e is:

A(e) = 6 *e².

The rate of change is:

A'(e) = 2 * 6 * e

The average rate of change between 3 in and 5 in is:

r  = (A(5in) + A(3in))/2 = (2*6*5in + 2*6*3in)/2 = 48in

Now, the options are given in:

"squere inches per inch"

This is written as:

in^2/in = in.

Then we can write our above rate as:

r = 48in = 48in^2/in = 48 square inches per inch.

Learn more about area

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