Determine the intervals on which f(x) is x>0 and on which f(x) is x<0.
1 answer:
Answer:
- f(x) > 0 for (-2.203, -1) U (2.203, ∞)
- f(x) < 0 for (-∞, -2.203) U (-1, 2.203)
Step-by-step explanation:
A graph shows real zeros at ±2.203 and -1. The value of f(x) changes sign at each of these.
The positive leading coefficient indicates the graph trends generally upward, so the function will be positive in intervals with an even number of zeros to the right.
<h3>f(x) positive</h3>There are an even number of zeros to the right of x = 2.203 and the interval (-2.203, -1).
f(x) is positive in the intervals (-2.203, -1) or (2.203, ∞).
<h3>f(x) negative</h3>The function will be negative where it is not positive (except at the zeros)
f(x) is negative in the intervals (-∞, -2.203) or (-1, 2.203).
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<em>Additional comment</em>
The graph shows the only rational real root of the function is x=-1. Using synthetic division to reduce the polynomial, we find ...
f(x) = (x +1)(x^4 -3x^2 -9)
The remaining factor is a quadratic in x^2, which has roots ...
x = ±√(1.5 ±√11.25)
The real roots are approximately ±2.20320266118. The value 2.203 used above is a stand-in for the exact value √(1.5 +√11.25)).
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Answer:
The critical value of <em>z</em> for 99% confidence interval is 2.5760.
The 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).
Step-by-step explanation:
Let <em>X</em> = number of lightning strikes on each day.
A random sample of <em>n</em> = 23 days is selected to observe the number of lightning strikes on each day.
The random variable <em>X</em> has a sample mean of, and the population standard deviation,
.
The (1 - <em>α</em>)% confidence interval for population mean <em>μ</em> is:
Compute the critical value of <em>z</em> for 99% confidence interval is:
*Use a <em>z</em>-table.
The critical value of <em>z</em> for 99% confidence interval is 2.5760.
Compute the 99% confidence interval for population mean number of lightning strike as follows:
Thus, the 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).
The 99% confidence interval for population mean number of lightning strike implies that the true mean number of lightning strikes lies in the interval (7.83 mn, 8.37 mn) with 0.99 probability.