What is 3/4× 4/5÷1/4÷1/2
1 answer:
You might be interested in
Answer:
(a) Decreasing on (0, 1) and increasing on (1, ∞)
(b) Local minimum at (1, 0)
(c) No inflection point; concave up on (0, ∞)
Step-by-step explanation:
ƒ(x) = x² - x – lnx
(a) Intervals in which ƒ(x) is increasing and decreasing.
Step 1. Find the zeros of the first derivative of the function
ƒ'(x) = 2x – 1 - 1/x = 0
2x² - x -1 = 0
( x - 1) (2x + 1) = 0
x = 1 or x = -½
We reject the negative root, because the argument of lnx cannot be negative.
There is one zero at (1, 0). This is your critical point.
Step 2. Apply the first derivative test.
Test all intervals to the left and to the right of the critical value to determine if the derivative is positive or negative.
(1) x = ½
ƒ'(½) = 2(½) - 1 - 1/(½) = 1 - 1 - 2 = -1
ƒ'(x) < 0 so the function is decreasing on (0, 1).
(2) x = 2
ƒ'(0) = 2(2) -1 – 1/2 = 4 - 1 – ½ = ⁵/₂
ƒ'(x) > 0 so the function is increasing on (1, ∞).
(b) Local extremum
ƒ(x) is decreasing when x < 1 and increasing when x >1.
Thus, (1, 0) is a local minimum, and ƒ(x) = 0 when x = 1.
(c) Inflection point
(1) Set the second derivative equal to zero
ƒ''(x) = 2 + 2/x² = 0
x² + 2 = 0
x² = -2
There is no inflection point.
(2). Concavity
Apply the second derivative test on either side of the extremum.
The function is concave up on (0, ∞).
Answer:
a) There is a 18.73% probability that exactly two students use credit cards because of the rewards program.
b) There is a 71.62% probability that more than two students use credit cards because of the rewards program.
c) There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.
Step-by-step explanation:
There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this problem by the binomial distribution.
Binomial probability
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
In this problem, we have that:
10 student are sampled, so
34% of college students say they use credit cards because of the rewards program, so
(a) exactly two
This is P(X = 2).
There is a 18.73% probability that exactly two students use credit cards because of the rewards program.
(b) more than two
This is .
Either a value is larger than two, or it is smaller of equal. The sum of the decimal probabilities must be 1. So:
In which
So
There is a 71.62% probability that more than two students use credit cards because of the rewards program.
(c) between two and five inclusive
This is:
There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.