Answer:
0 is an inflection point
1/4 is a local maximum.
Step-by-step explanation:
To begin with you find the first derivative of the function and get that
![h'(x) = 3x^2 - 12x^3](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%203x%5E2%20-%2012x%5E3)
to find the critical points you equal the first derivative to 0 and get that
![3x^2 - 12x^3 = 0, x = 0,1/4](https://tex.z-dn.net/?f=3x%5E2%20-%2012x%5E3%20%3D%200%2C%20x%20%3D%20%200%2C1%2F4)
To find if they are maximums or local minimums you use the second derivative.
![h''(x) = 6x-36x^2](https://tex.z-dn.net/?f=h%27%27%28x%29%20%3D%206x-36x%5E2)
since
is neither an inflection point, and since
then 1/4 is a maximum.
Answer:
7.28 miles
Step-by-step explanation:
Suppose the distance at closest approach is represented by x. Then the distance to the point of closest approach at the first sighting is ...
d1 = x·tan(62°)
At the second sighting, the distance to the point of closest approach is ...
d2 = x·tan(38°)
The difference of these distances is 8 miles, so we have ...
d1 -d2 = 8 = x(tan(62°) -tan(38°))
Dividing by the coefficient of x, we find ...
x = 8/(tan(62°) -tan(38°)) ≈ 7.2764 . . . . miles
The point of closest approach is about 7.28 miles from the landmark.
The answer is CD = √3
This is because of the fact that a 30-60-90 right triangle has proportions of 1-√3-2 based on the length opposite of the angle. Since we are given the segment opposite to the right angle as 2, we know that we can use the base numbers for the proportions to find the rest. Since CD is opposite of the 60 degree angle, it must be √3.