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? 48 square inches per inch
54 square inches per inch
66 square inches per inch
96 square inches per inch

48 square inches per inch

Step-by-step explanation:

The surface area of a cube of sidelength e is:

A(e) = 6*e^2.

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.

1 3 5

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