(a) Use differentiation to find a power series representation for f(x) = 1 (6 + x)2 . f(x) = [infinity] n = 0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for f(x) = 1 (6 + x)3 . f(x) = [infinity] n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for f(x) = x2 (6 + x)3 . f(x) = [infinity] n = 2 What is the radius of convergence, R? R =

The correct options are;

The equation of the function is 2·y = -25·x + 200

The equation of the function is y = -25/2·x  + 100

The x-intercept of the function is (8, 0)

Step-by-step explanation:

From the graph of the function, the y-intercept is observed at (0, 100), the x-intercept occurs at (8, 0)

Therefore, we have the slope, m given by the following relation

Where:

y₁ = 100

x₁ = 0

y₂ = 0

x₂ = 8

Which gives;

The equation in slope can be found as follows

y - 100 = -12.5×(x - 0)

y = -12.5·x  + 100 = -25/2·x  + 100

Multiplying by 2 gives;

2·y = -25·x + 200

25·x + 2·y =  200

Therefore, the correct options are;

The equation of the function is 2·y = -25·x + 200

The equation of the function is y = -25/2·x  + 100

The x-intercept of the function is (8, 0).