How many lines of symmetry?
2 answers:
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Answer:
f(x) is increasing in the intervals (-∞,-4) and (9,∞)
f(x) is decreasing in the ingercal (-4,9)
The local extrema is:
local max at (-4,496)
and local min at (9,-1701)
Step-by-step explanation:
In order to solve this problem we must start by finding the derivative of the provided function, which we can find by using the power rule.
if then
so we get:
in order to find the critical points we mus set the derivative equal to zero, since the local max an min will happen when the slope of the tangent line to the given point is zero, so we get:
we can solve this by factoring, so let's factor that equation:
6(x+4)(x-9)=0
we can now set each of the factors equal to zero so we get:
x+4=0 and x-9=0
when solving each for x we get that:
x=-4 and x=9
These are our critical points, now we can build the possible intervals we are going to use to determine where the function will be increasing and where it will be decreasing:
(-∞,-4), (-4,9) and (9,∞)
so now we need to test these intervals in the derivative to see if the graph will be increasing or decreasing in the given intervals. So let's pick x=-5 for the first one, x=0 for the second one and x=10 for the third one.
When evaluating them into the first derivative we get that:
f'(-5)=84, this is a positive answer so it means that the function is increasing in the interval (-∞,--4)
f'(0)=-216, this is a negative anser so it means that the function is decreasing in the interval (-4,9)
f'(10)=84, this is a positive answer so it means that the function is increasing in the interval (9,∞)
Now, for the local extrema, we can see that at x=-4, the function it's increasing on the left of this point while it's decreasing to the right, which means that there will be a local maximum at x=-4, so the local max is the point (-4,496)
We can see that at x=9, the function it's decreasing on the left of this point while it's increasing to the right, which means that there will be a local minimum at x=-9, so the local min is the point (9,-1701)
Answer:
The probability distribution is shown below.
Step-by-step explanation:
The urn consists of 8 white (<em>W</em>), 4 black (<em>B</em>) and 2 orange (<em>O</em>) balls.
The winning and losing criteria are:
- Win $2 for each black ball selected.
- Lose $1 for each white ball selected.
There are 8 + 4 + 2 = 14 balls in the urn.
The number of ways to select two balls is, ways.
The distribution of amount won or lost is as follows:
Outcomes: WW WO WB BB BO OO
X: -2 -1 1 4 2 0
Compute the probability of selecting 2 white balls as follows:
The number of ways to select 2 white balls is, ways.
The probability of WW is,
Compute the probability of selecting 1 white ball and 1 orange ball as follows:
The number of ways to select 1 white ball and 1 orange ball is, ways.
The probability of WO is,
Compute the probability of selecting 1 white ball and 1 black ball as follows:
The number of ways to select 1 white ball and 1 black ball is, ways.
The probability of WB is,
Compute the probability of selecting 2 black balls as follows:
The number of ways to select 2 black balls is, ways.
The probability of BB is,
Compute the probability of selecting 1 black ball and 1 orange ball as follows:
The number of ways to select 1 black ball and 1 orange ball is, ways.
The probability of BO is,
Compute the probability of selecting 2 orange balls as follows:
The number of ways to select 2 orange balls is, ways.
The probability of OO is,
The probability distribution of <em>X</em> is:
Outcomes: WW WO WB BB BO OO
X: -2 -1 1 4 2 0
P (X): 0.3077 0.1758 0.3516 0.0659 0.0879 0.0110