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laila [671]
3 years ago
15

plant A is 18 inches tall after one week 36 inches tall after two weeks 56 inches tall after three weeks plant B is 18 inches ta

ll after one week 36 inches tall after two weeks 54 inches tall after three weeks which situation represensts a proportional relationship between the plants height and number of weeks
Mathematics
1 answer:
Afina-wow [57]3 years ago
3 0
Plants increase by 18 inches every week
proportion would be 18inches/week
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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
What is 53 divided by 30?
vlada-n [284]

Answer:

1.76666666666666666

3 0
3 years ago
Read 2 more answers
Help help help help help
aev [14]
First one, cause it is to dramatic!!!!!!!!!!!!!!!


hope this helps, may I have brainliest?
7 0
3 years ago
Use the triangle below and the given trigonometric ratio to determine which angle in the triangle below is
MrRa [10]
Answer: Angle 2

The 7.5 cm side is opposite angle 2, so opposite = 7.5
The 18 cm side is adjacent to angle 2, so adjacent = 18

Therefore, tan(angle 2) = opposite/adjacent = 7.5/18
Replace "angle 2" with "A" and we have tan(A) = 7.5/18
7 0
3 years ago
determine the event space for rolling a sum of 12 with two dice. how many elements are in the event space?
WARRIOR [948]

Answer: 1

Step-by-step explanation:

Only one element is in the event space for rolling the sum of 12 with two dice

(6,6)

If you must roll the sum of 12 with two dice, you must have rolled 6 in the two dice

7 0
3 years ago
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