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Hi there!
We can find the values of x for which f(x) is decreasing by finding the derivative of f(x):
Taking the derivative gets:
Find the values for which f'(x) < 0 (less than 0, so f(x) decreasing):
0 = -8/x³ - 2
2 = -8/x³
2x³ = -8
x³ = -4
Another critical point is also where the graph has an asymptote (undefined), so at x = 0.
Plug in points into the equation for f'(x) on both sides of each x value to find the intervals for which the graph is less than 0:
f'(1) = -8/1 - 2 = -10 < 0
f'(-1) = -8/(-1) - 2 = 6 > 0
f'(-2) = -8/-8 - 2 = -1 < 0
Thus, the values of x are:
Answer:
The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>The probability distribution is:</em>
<em>x P(x) </em>
<em> 0 0.30 </em>
<em>1 0.40 </em>
<em>2 0.20 </em>
<em>3 0.06 </em>
<em>4 0.04</em>
The mean can be calculated as:
(pi is the probability of each class, Xi is the number of topping in each class)
The standard deviation is calculated as: