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KonstantinChe [14]
2 years ago
10

Please help aleks sucks will give brainliest PLEASE HELP ME! :(

Mathematics
1 answer:
vredina [299]2 years ago
3 0

the answer is x > -2

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Consider the following function. f(x) = 2x3 + 9x2 − 24x (a) Find the critical numbers of f. (Enter your answers as a comma-separ
viktelen [127]

Answer:

(a) The critical number of f(x) are x=-4, 1

(b)

  • Increasing for (-\infty, -4)
  • Decreasing for (-4, 1)
  • Increasing for  (1, \infty)

(c)

  • relative maximum (-4, 112)
  • relative minimum (1, -13)

Step-by-step explanation:

(a) The critical numbers of a function are given by finding the roots of the first derivative of the function or the values where the first derivative does not exist. Since the function is a polynomial, its domain and the domain of its derivatives is (-\infty, \infty). Thus:

\frac{df(x)}{dx}  = \frac{d(2x^3+9x^2-24x)}{dx} =6 x^2+18x -24\\6 x^2+18x -24=0\\\boxed{x=-4, x=1}

(b)

  • A function f(x) defined on an interval is monotone increasing on (a, b) if for every x_1, x_2 \in (a, b): x_1 implies f(x_1)
  • A function f(x) defined on an interval is monotone decreasing on (a, b) if for every x_1, x_2 \in (a, b): x_1 implies f(x_1)>f(x_2)

Combining  the domain (-\infty, \infty) with the critical numbers we have the intervals (-\infty, -4), (-4, 1) and (1, \infty). Note that any of the points are included, in the case of the infinity it is by definition and the critical number are never included because the function monotony is not defined in the critical points, i.e. it is not monotone increasing or decreasing. Now, let's check for the monotony in each interval, for this, we check for the sign of the first derivative in each interval. Evaluating in each interval the first derivative (one point is enough), we obtain the monotony of the function to be:

  • Increasing for (-\infty, -4)
  • Decreasing for (-4, 1)
  • Increasing for  (1, \infty)

(c) From the values obtained in (a) so the relative extremum are the points (-4, 112) and (1, -13). The y-values are found by evaluating the critical numbers in the original function. Since the first derivative decreases after passing through  x=-4 and increases after passing through the point x=1 we have:

  • relative maximum (-4, 112)
  • relative minimum (1, -13)

3 0
3 years ago
Help in math please, thank you
madam [21]
6/11

The square root of 36 is 6, and the square root of 121 is 11, giving you 6/11
5 0
2 years ago
Read 2 more answers
a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the proba
Aleksandr-060686 [28]
5 red, 3 yellow, and 2 blue....for a total of 10 marbles

P(first one being blue) = 2/10 which reduces to 1/5
not replaced
P(second one is blue) = 1/9...because u already pick a blue, meaning there is only 1 left, and there is one less marble, so there is a total of 9 marbles.

P(both events happening) = 1/5 * 1/9 = 1/45 <==
7 0
3 years ago
Analyze the diagram below and answer the question that follows. If &lt;10 and &lt;15 are congruent, which lines are parallel? A.
yanalaym [24]

If angle 10 and 15 are congruent ( the same) that would mean lines a and b would need to be parallel with each other because that have the same angles.

The answer ic C.

7 0
3 years ago
Read 2 more answers
Which is the equation of the line that passes through the point (-5, -2)
Lilit [14]

Answer:

F) y=3x+13

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=3(x-(-5))

y+2=3(x+5)

y=3x+15-2

y=3x+13

5 0
2 years ago
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