a company makes computer chips from square wafers of silicon. it wants to keep the side length of a wafer…

a company makes computer chips from square wafers of silicon. it wants to keep the side length of a wafer very close to 11 mm and it wants to know changes when the side length x changes. find a(11). a(11) = mm²/mm explain the meaning of a(11) in this situation. a(11) represents the rate at which the area is increasing with respect to the side length as a reaches 22 mm². a(11) represents the rate at which the area is increasing as x reaches 22 mm. a(11) represents the rate at which the side length is increasing with respect to the area as x reaches 11 mm. a(11) represents the area as the side length reaches 11 mm. a(11) represents the rate at which the area is increasing with respect to the side length as x reaches 11 mm. need help? read it watch it

a company makes computer chips from square wafers of silicon. it wants to keep the side length of a wafer very close to 11 mm and it wants to know changes when the side length x changes. find a(11). a(11) = mm²/mm explain the meaning of a(11) in this situation. a(11) represents the rate at which the area is increasing with respect to the side length as a reaches 22 mm². a(11) represents the rate at which the area is increasing as x reaches 22 mm. a(11) represents the rate at which the side length is increasing with respect to the area as x reaches 11 mm. a(11) represents the area as the side length reaches 11 mm. a(11) represents the rate at which the area is increasing with respect to the side length as x reaches 11 mm. need help? read it watch it

Answer

Explanation:

Step1: Find area formula

The area $A$ of a square with side - length $x$ is $A(x)=x^{2}$.

Step2: Differentiate the area function

Using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$, we have $A'(x)=\frac{d}{dx}(x^{2}) = 2x$.

Step3: Evaluate the derivative at $x = 11$

Substitute $x = 11$ into $A'(x)$: $A'(11)=2\times11 = 22$.

The meaning of $A'(11)$: The derivative of a function represents the rate of change of the function. Here, $A(x)$ is the area of the square wafer and $x$ is the side - length. So $A'(11)$ represents the rate at which the area is increasing with respect to the side length as $x$ reaches $11$ mm.

Answer:

$A'(11)=22$ mm²/mm The correct option is: $A'(11)$ represents the rate at which the area is increasing with respect to the side length as $x$ reaches $11$ mm.