Question

Find the maximum and minimum values of the function

y=2cos(theta)+9sin(theta) on the interval [0,2] by comparing values at the
critical points and endpoints.

Answer 1

To find the max and min values of the function y = 2cos(θ) + 9sin(θ), we need to evaluate it at critical points where the derivative is zero and at the endpoints of the interval [0, 2π].

Step-by-step explanation:

To find the maximum and minimum values of the function y = 2cos(θ) + 9sin(θ), we need to evaluate this function at critical points and the endpoints of the given interval [0, 2π].

First, we need to find the critical points by taking the derivative of the function with respect to θ and setting it to zero. The first derivative of the function is •y'(θ) = -2sin(θ) + 9cos(θ). We would set this equal to zero to solve for θ, but in the given interval, the critical points will be at points where cos(θ) = 0 or sin(θ) = 0, within the interval [0, 2π].

Next, we evaluate the function at the endpoints of the interval, θ = 0 and θ = 2π, and at the critical points found previously. By doing this, we can compare the values to determine which ones are the maximum and minimum values of the function on the given interval.