Question

Calculate the slope, m, of the tangent line to the rational function f at x = 10.

f(x) = 2/(x - 6)
Use decimal notation. Give your answer in exact form.

Answer 1

The slope of the tangent line to the rational function f at x = 10 is -0.5.

Step-by-step explanation:

To find the slope, m, of the tangent line to the rational function f at x = 10, we need to take the derivative of the function with respect to x and evaluate it at x = 10. The given function is f(x) = 2/(x - 6).

To find the derivative, we can use the quotient rule. The derivative of f(x) = 2/(x - 6) is given by f'(x) = (-2)/(x - 6)^2. Evaluating the derivative at x = 10, we get f'(10) = (-2)/(10 - 6)^2 = (-2)/4 = -0.5.

Therefore, the slope of the tangent line to the rational function f at x = 10 is -0.5.