Question

Let f(x) = cos(3θ). Find the slope of the tangent line for the curve at θ = π/3.

Answer 1

The slope of the tangent line for the curve f(x) = cos(3θ) at θ = π/3 is found by taking the derivative of cos(3θ), which is -3sin(3θ), and evaluating it at θ = π/3. This results in a slope of 0 for the tangent line at the specified point.

Step-by-step explanation:

To find the slope of the tangent line for the curve f(x) = cos(3θ) at θ = π/3, we must first compute the derivative of f(x) with respect to θ, which gives us f'(x). The derivative of cos(3θ) is -3sin(3θ). Substituting θ = π/3 into f'(x) provides us with the slope of the tangent line at that point.

f'(x) at θ = π/3 is:

-3sin(3(π/3))

-3sin(π)

-3(0)

Thus, the slope of the tangent line at θ = π/3 is 0.