Area of the circle and circumference of the circle .

(a)

Solve the equation for .

Substitute in .

.

is represent the area of circle as a function of its circumference.

(b)

Find .

Substitute in .

.

Find .

Substitute in .

.

(c)

Observe the results of (b) :

As the circumference increases, the value of the expression increases, therefore the area will also increases.

(a) The function is .

(b) and  .

(c) As the circumference increases, the area will also increases.