Calculus(20/09/2024)

 

In search of his fortune, a prospector named Jack had heard tales of a legendary gold mine hidden deep in the mountains. Inspired by stories of riches, he set out to explore three promising locations: Point A, Point B, and Point C. 

Using his metal detector, he discovered at point A, a signal modeled by the function f(t)=2sin⁡(3t)+4tf(t) = 2\sin(3t) + 4t; at Point B, the signal was represented by g(t)=3sin⁡(2t)+5tg(t) = 3\sin(2t) + 5t; and at Point C, the function was h(t)=4sin⁡(t)+2th(t) = 4\sin(t) + 2t

Jack knew that the greater the difference between the maximum value of the derivative of the signal and a threshold of 8, the more likely he was to stumble upon gold. Select the correct alternative.

a) He is more likely to find gold at Point A.

b) He is more likely to find gold at Point B.

c) He is more likely to find gold at Point C.

d) He is equally likely to find gold at all points.

e) None of the above.

Original idea by: João Vitor Baptista Moreira

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