A company makes computer chips from square wafers of silicon. It wants to keep t

Question

A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 15 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes Find A'(15). A'(15) = mm^2/mm Explain the meaning of A'(15) in the situation. A'(15) represents the area as the side length reaches 15 mm. A'(15) represents the rate at which the area is increasing with respect to the side length as A reaches 30 mm^2. A'(15) represents the rate at which the side length is increasing with respect to the area as x reaches 15 mm. A'(15) represents the rate at which the area is increasing as x reaches 30 mm. A'(15) represents the rate at which the area is increasing with respect to the SIDE length as x reaches 15 mm.

Explanation / Answer

Solution:

Then, the area function is...

A(x) = x^2

Differentiate the function to get...

A'(x) = 2x

If x = 15, then A'(15) = 30 mm^2/mm

This means that when x = 15 mm, an increase in x by just 1 mm will result in an increase of the area by approximately 30 mm^2

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