Answered

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Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?

Sagot :

The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.

What is the maximum and minimum value of the function?

The condition for the maximum will be

f(x)'' < 0

The condition for the minimum will be

f(x)'' > 0

Every summer, Richard plants a garden on a rectangular plot of land.

Last summer, Richard's garden measured 45 feet in length and 18 feet in width.

This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.

The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.

Length = (45 – x)

Width = (18 + 2x)

Then the maximum potential area of this year's resized garden will be

A(x) = (45 – x)(18 + 2x)

A(x) = 810 + 72x – 2x²

A(x) = 2(405 + 36x – x²)

For maximum potential, A'(x) = 0

    A'(x) = 0

36 - 2x = 0

       2x = 36

         x = 18

Then the maximum potential area will be

A(x) = 2(405 + 36 × 18 – 18²)

A(x) = 1458

More about the maximum and minimum value of the function link is given below.

https://brainly.com/question/13581879

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