Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing? (–∞, –3) (–∞, 2) (–3, ∞) (
2 answers:
Answer:
The interval over which the graph is decreasing is;
(-∞, -3)
Explanation:
The given function is f(x) = 2·(x + 3)² + 2
By expanding the function, we have;
2·x² + 12·x + 20
From the characteristics of a quadratic equation, we have;
The shape of a quadratic equation = A parabola
The coefficient of x² = +2 (positive), therefore the parabola opens up
The parabola has a minimum point
Points to the left of the minimum point are decreasing
The minimum point is obtained as the x-coordinate value when f'(x) = 0
∴ f'(x) = d(2·x² + 12·x + 20)/dx = 4·x + 12
At the minimum point, f'(x) = 4·x + 12 = 0
∴ x = -12/4 = -3
Therefore;
The graph is decreasing over the interval from -infinity (-∞) to -3 which is (-∞, -3)
Please find attached the graph of the function created with Microsoft Excel
The graph is decreasing over the interval (-∞, -3).
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Answer:
The answer to this question can be defined as follows:
Explanation:
Its Permute-with-all method, which doesn't result in a consistent randomized permutation. It takes into account this same permutation, which occurs while n=3. There's many 3 of each other, when the random calls, with each one of three different values returned and so, the value is= 27. Allow-with-all trying to call possible outcomes as of 3! = 6
Permutations, when a random initial permutation has been made, there will now be any possible combination 1/6 times, that is an integer number m times, where each permutation will have to occur m/27= 1/6. this condition is not fulfilled by the Integer m.
Yes, if you've got the permutation of < 1,2,3 > as well as how to find out design, in which often get the following with permute-with-all chances, which can be defined as follows:
Although these ADD to 1 none are equal to 1/6.