Answer:Function assigns the value of each element of one set to another element of another set. At point, , function A will be maximum.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Assume that the radius of the semicircle is r, while the length of the rectangle is L. therefore, 2r or the diameter of the width of the rectangle.
Now, the perimeter of the window consists of two lengths, one width, and length of the semicircle, therefore,
The length of the window can be written as,
The area of the window can be written as,
Substituting the value of the length of the window,
Finding the derivative of the Area, A with respect to the radius, r.
Equating the derivative with 0,
Thus, if then A'>0 therefore, the function A is increasing, and when then A'<0 therefore, the function A is decreasing.
Hence, this means that at the point the function A will be maximum.
Function assigns the value of each element of one set to another element of another set. At point, , function A will be maximum.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Assume that the radius of the semicircle is r, while the length of the rectangle is L. therefore, 2r or the diameter of the width of the rectangle.
Now, the perimeter of the window consists of two lengths, one width, and length of the semicircle, therefore,
The length of the window can be written as,
The area of the window can be written as,
Substituting the value of the length of the window,
Finding the derivative of the Area, A with respect to the radius, r.
Equating the derivative with 0,
Thus, if then A'>0 therefore, the function A is increasing, and when then A'<0 therefore, the function A is decreasing.
Hence, this means that at the point the function A will be maximum.
Function assigns the value of each element of one set to another element of another set. At point, , function A will be maximum.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Assume that the radius of the semicircle is r, while the length of the rectangle is L. therefore, 2r or the diameter of the width of the rectangle.
Now, the perimeter of the window consists of two lengths, one width, and length of the semicircle, therefore,
The length of the window can be written as,
The area of the window can be written as,
Substituting the value of the length of the window,
Finding the derivative of the Area, A with respect to the radius, r.
Equating the derivative with 0,
Thus, if then A'>0 therefore, the function A is increasing, and when then A'<0 therefore, the function A is decreasing.
Hence, this means that at the point the function A will be maximum.
Explanation: