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zoejacobs2002
18.12.2019 •
Mathematics
The same boy flies the kite that is now 100 feet above the ground. if the string is pulled out at 10ft/min because the wind carries the kite horizontally away from the boy, what is the rate of change of the angle the kite makes with the vertical when the angle is 30 degrees?
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Ответ:
(a) Increasing in the interval (-623, 2) and (623, ∞)
f is decreasing in the interval (∞, -623) and (2, - 623).
(b) Local maximum is f = 2 .
2 local minima f = -623.
Step-by-step explanation:
f(x) = x^4 - 50x^2 + 2
Finding the derivative:
f'(x) = 4x^3 - 100x
This = 0 at a turning point:
4x(x^2 - 25) = 0
x = 0, x + -5, 5.
Find the second derivative:
f"(x) = 12x^2 - 100
When x = 0 f(x) = 2
When x = 0, f"(x) is negative so the point (0, 2) is a maximum .
When x = -5, f"(x) is positive . Also positive when x = 5.
So the 2 local minimums are (-5, (-5)^4 - 50(-5)^2 + 2) = (-5, -623) and
(5, -623).