Relative extrema occur where the derivative is zero (at least for your polynomial function).
So taking the derivative we get
<span>20<span>x3</span>−3<span>x2</span>+6=0
</span><span>
This is a 3rd degree equation, now if we are working with complex numbers this equation is guaranteed to have 3 solutions by the fundamental theorem of algebra. But the number of real roots are 1 which can be found out by using Descartes' rule of signs. So the maximum number of relative extrema are 1.</span>
Find where the equation is undefined ( when the denominator is equal to 0.
Since they say x = 5, replace x in the equation see which ones equal o:
5-5 = 0
So we know the denominator has to be (x-5), this now narrows it down to the first two answers.
To find the horizontal asymptote, we need to look at an equation for a rational function: R(x) = ax^n / bx^m, where n is the degree of the numerator and m is the degree of the denominator.
In the equations given neither the numerator or denominators have an exponent ( neither are raised to a power)
so the degrees would be equal.
Since they are equal the horizontal asymptote is the y-intercept, which is given as -2.
This makes the first choice the correct answer.
N² - 49 = 0
<u> + 49 + 49</u>
n² = 49
n = <u>+</u>7
The solution to the problem is {7, -7}.
The jar has 6+5=11 marbles.
We have to find the probability of the following event:
1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red
2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)
The probability of the first event is:
The probability of the second event is:
The probability of the both events to happen is:
X = 47
you subtract 133 from 180
