Question

Let g be the function given by g(t) 100 + 20sin (πt/2) + 10cos (πt/6)

For 0 ≤ t ≤ 8, g is decreasing most rapidly when t =

A) 0.949
B) 2.017
C) 3.106
D) 5.965
E) 8.000

Answer 1

To find when the function g(t) = 100 + 20sin(πt/2) + 10cos(πt/6) is decreasing most rapidly, take the derivative of g(t) with respect to t, set it equal to zero, and solve for t.

Step-by-step explanation:

To find when the function g(t) = 100 + 20sin(πt/2) + 10cos(πt/6) is decreasing most rapidly, we need to find the value of t where the derivative of g(t) is equal to zero. Take the derivative of g(t) with respect to t and set it equal to zero. Solve for t to find the point where g(t) is decreasing most rapidly. Taking the derivative, we get g'(t) = (10π/2)cos(πt/2) - (10π/6)sin(πt/6). Set g'(t) equal to zero and solve for t to find the answer.