Answer:
Step-by-step explanation:
cartesian plane :
quadrant 1 : both x and y are positive
quadrant 2 : x is negative, y is positive
quadrant 3 : both x and y are negative
quadrant 4 : x is positive and y is negative
(-2,4)......we have x is negative and y is positive...so we are in quadrant 2
(3,-1)....we have x is positive and y is negative...in quadrant 4
(-1,0) ...if u have a 0 in ur points, they do not lie in any quadrant because they are located on an axis....this is located on axis x
(1,2)....both are positive....located in quadrant 1
(-3,-5)...both are negative.....quadrant 3
![y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\ y''(0)=20\cdot0^3=0](https://tex.z-dn.net/?f=y%3Dx%5E5-3%5C%5C%20y%27%3D5x%5E4%5C%5C%5C%5C%205x%5E4%3D0%5C%5C%20x%3D0%5C%5C%200%5Cin%20%5B-2%2C1%5D%5C%5C%5C%5C%20y%27%27%3D20x%5E3%5C%5C%5C%5C%0Ay%27%27%280%29%3D20%5Ccdot0%5E3%3D0)
The value of the second derivative for
is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of
is always positive for
. That means at
there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval
![[-2,1]](https://tex.z-dn.net/?f=%5B-2%2C1%5D)
.
The function
is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.
Answer:
1/9
Step-by-step explanation:
For these questions, you have to first find the probability of each event individually occuring then multiply these two probabilities together. So, lets first find the probability of Event 1 occuring (rolling a number higher than 1). On a dice, we know that there are 6 numbers (1, 2, 3, 4, 5, 6) of which the numbers 5 and 6 are higher than 4. Therefore, the proability of Event 1 occuring is 2/6 = 1/3. Now, we find the probability of event 2 occuring.
We know that there are 3 options on the spinner that the arrow can land on. It is also evident that they all have the same chance of landing on it. Therefore, the possibility is 1/3.
Now that we have both of our probabilities, we multiply the answer together.
Therefore, our answer will be:
1/3 x 1/3, which gives 1/9.
