# S = 6x^2 is the surface area of a cube. Find the exact change in surface area when x is increased...

## Question:

{eq}S = 6x^2 {/eq} is the surface area of a cube. Find the exact change in surface area when x is increased from 6 cm to 6.1 cm.

## Evaluating a function:

we are asked to measure the change in the function value as the independent variable changes. We can evaluate the function at the two points and take the difference. Or we could write an expression for the difference in the function value as a function of the independent variable.

Surface area of a cube:

{eq}S = 6x^2 {/eq}

Let {eq}S_1 {/eq} be the surface area at {eq}x = x_1 = 6 \; \text {cm} {/eq}

And let {eq}S_2 {/eq} be the surface area at {eq}x = x_2 = 6.1 \; \text {cm} {/eq}

Then

{eq}\begin{align} S_2 - S_1 &= 6 x_2^2 - 6x_1^2\\ &= 6(x_2^2 - x_1^2)\\ &= 6 (x_2 + x_1) (x_2 - x_1)\\ &= 6 (6.1 + 6) (6.1 -6)\\ &= 6(12.1)(0.1)\\ &= (72.6)(0.1)\\ &= 7.26 \; cm^2 \end{align} {/eq}