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Answer:
A 12 in diameter will reward you with the largest slice of pizza.
Step-by-step explanation:
Let be the radius and
be the angle of a circle.
According with the graph, the area of the sector is given by
The arc lenght of a circle with radius and angle
is
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
We need to express the area as a function of one variable, to do this we use the above equation and we solve for
Next, we substitute this equation into the area equation
The domain of the area is
To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.
To check if is a maximum we use the Second Derivative test
if and
, then f(x) has a local maximum at x = c.
The second derivative is
Because the largest slice is when r = 6 in.
The diameter of the pizza is given by
A 12 in diameter will reward you with the largest slice of pizza.
