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The function f(x) = xπ−−√ gives the diameter, in inches, of a proposed spherical sculpture with a surface area of x square inches. The artist making the sculpture wants to know how the diameter changes if the surface area is increased. What is the average rate of change for the function as the surface area changes from 12.6 in.2 to 28.3 in.2? Round your answer to the nearest hundredth of an inch.

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oladayoademosu

Answer:

The average rate of change of f(x) = 3.14 inches⁻¹

The change in f(x) = 49.32 in

Step-by-step explanation:

The surface area of the spherical sculpture = x and its diameter f(x) = πx.

The average rate of change of f(x) as x changes is df(x)/dx = π = 3.14

Now the change in diameter Δf(x) = df(x) = (df(x)/dx)dx = πdx  

dx = Δx = 28.3 in² - 12.6 in² = 15.7 in²

df(x) = π × 15.7 = 49.32 in

The average rate of change of f(x) = 3.14inches⁻¹.

The change in f(x) = 49.32 in

We have given that,

The function f(x) = xπ−−√ gives the diameter, in inches, of a proposed spherical sculpture with a surface area of x square inches.

What is the formula for the diameter of the spherical sculpture?

diameter f(x) = πx.

The surface area of the spherical sculpture = x

The average rate of change of f(x) as x changes is df(x)/dx

π = 3.14

Therefore differentiate the

f(x)=πx.

Now the change in diameter

Δf(x) = df(x)

= (df(x)/dx)dx

= πdx  

dx = Δx

= 28.3 in² - 12.6 in²

= 15.7 in²

df(x) = π × 15.7

= 49.32 in

Therefore, The average rate of change of f(x)= 49.32 in inches⁻¹.

To learn more about the rate change visit:

https://brainly.com/question/25184007

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