9514 1404 393
Answer:
- relative minimum -6√3 at x = -√3
- relative maximum 6√3 at x = √3
- decreasing on x < -√3 and x > √3
- increasing on -√3 < x < √3
- see below for a graph
Step-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
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Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
Answer:

Step-by-step explanation:
Here, the given expression is

Now, simplifying the brackets, we get
= 
Now, operate on the like terms.
= 
=
Hence, the given expression is simplified to the quadratic equation
Answer:
The expected value for the number of inspections until a defective unit is found 17.
Step-by-step explanation:
Percentage of defective microchips = 6%
Let the total number of inspection = x
number of defective microchip = 1
As we know
1/x = 6%
1/x = 0.06
x = 1/ 0.06
x = 16.67 inspections
x = 17 ( rounded off to nearest whole number )
17 inspection is done until the defective microchip is found.
S≤12 s is equal to or less than 12 because 20 minus 12 equals 8. The class will still be held. Any number less than 12, there will be more students than 8 and the class will still be held.
Answer:
B. 28 hours
Step-by-step explanation:
GIVEN :- <em>Time taken by family to travel 600 km is 8 hours</em>
CALCULATIONS :-
<em>To calculate the time to travel 2100 km, we need to calculate distance traveled in 1 hour</em>
<em>Distance traveled in 1 hour = 600 km ÷ 8</em>
<em> = 75 km</em>
<em>Time required to travel 2100 km = 2100 ÷ 75</em>
<em> = </em><em>28 hours</em>
Therefore time required to travel 2100 km is 28 hours.