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Vaselesa [24]
3 years ago
13

Will Mark Brilliant!

Mathematics
1 answer:
pochemuha3 years ago
8 0

Answer:

87.8

Step-by-step explanation:

I assume you know how to do this so I didn't show any steps. Have a nice night. :)

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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 a counterexample to this claim?
yan [13]
Answer: B
Explanation: 9 is the only odd number meaning it’s contradicting the claim that all perfect squares are even since 9 isn’t even. a 3x3 square would be 9 but its also perfect explaining how not all perfect squares are even.
5 0
3 years ago
9.3-t=-1.6 what is the value of t?
vovangra [49]

Answer:

t = 10.9

Step-by-step explanation:

9.3-t=-1.6

Subtract 9.3 from each side

9.3-t-9.3=-1.6-9.3

-t =-10.9

Multiply each side by -1 to find t

t = 10.9

8 0
3 years ago
Read 2 more answers
Please help me with this asap
Mice21 [21]

Answer:

I think the answer is A

hope this helps :3

sorry if im wrong

5 0
3 years ago
If f(x) = 2x² +5 and g(x)=x2-2, find (f-g)(x).
Rufina [12.5K]

Answer:D. x^2+7

Step-by-step explanation:

If f(x) = 2x² +5 and g(x)=x2-2, find (f-g)(x).A. x^2+3B. 3x^2+3C. 3x^2+7D. x^2+7

4 0
1 year ago
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