contestada

A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 20 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A'(20).

Respuesta :

muhammadalambsmathf1

Answer:

The answer is  40 mm^2 per mm

Step-by-step explanation:

The area of  a square with side length is  x

and

A(x) = [tex]x^2[/tex] ([tex]mm^2[/tex])

The Derivative of the area is the rate of change of the area.

so

[tex]A^{'[/tex](x) = 2x

and we have to find [tex]A^{'}[/tex](20)

so  we put x = 20 in the derivative of the area we get

[tex]A^{'}[/tex](20) = 2(20)

[tex]A^{'}[/tex](20) = 40 [tex]mm^2[/tex] per mm

that is we need

A'(20) = 40 [tex]mm^2[/tex] per mm.