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valentinak56 [21]
2 years ago
6

A function f is​ _____ on an open interval I​ if, for any choice of x1 and x2 in​ I, with 1 less than

Mathematics
1 answer:
Zepler [3.9K]2 years ago
3 0

Answer:

If f(x_1)\leq f(x_2) whenever x_1\leq x_2 f is <em>increasing</em> on I.

If f(x_1)\geq f(x_2) whenever x_1\leq x_2 f is <em>decreasing</em> on I.

Step-by-step explanation:

These are definitions for real-valued functions f:I→R. To help you remember the definitions, you can interpret them in the following way:

When you choose any two numbers x_1\leq x_2 on I and compare their image under f, the following can happen.

  • f(x_1)\leq f(x_2). Because x2 is bigger than x1, you can think of f also becoming bigger, that is, f is increasing. The bigger the number x2, the bigger f becomes.
  • f(x_1)\geq f(x_2). The bigger the number x2, the smaller f becomes so f is "going down", that is, f is decreasing.

Note that this must hold for ALL choices of x1, x2. There exist many functions that are neither increasing nor decreasing, but usually some definition applies for continuous functions on a small enough interval I.

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wolverine [178]

Answer:

286 cubes

Step-by-step explanation:

Find the area by multiplying the fractions. You get 71 1/2. Divide the area by 1/4 that determines your answer.

8 0
2 years ago
Whats 387 rounded to the nearests 100
torisob [31]
I rounded it and the answer is 400
4 0
3 years ago
Evaluate 3 to the 2nd power plus 7 times 2
Olin [163]

Hey there!

3^2 + 7 • 2

3^2 = 3 • 3 = 9

9 + 7 • 2

7 • 2 = 14

9 + 14 = 23

Answer: 23 ☑️

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

7 0
3 years ago
Read 2 more answers
A culture started with 3000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after
Vlad [161]
Hello Shannonrodrigue. You can solve this by setting up an exponential growth equation.

A = A_ob^t
3600 = 3000b^4

Now we solve for b
3600 = 3000b^4
\frac{3600}{3000} = \frac{3000b^{4}}{3000}
\frac{6}{5} = b^4
\sqrt[4]{\frac{6}{5}} = \sqrt[4]{b^4}
\sqrt[4]{\frac{6}{5}} = b

Now that we have found b, we can use the equation A = 3000b^t to predict how many bacteria will be present after 10 hours.
b = \sqrt[4]{\frac{6}{5}}
t = 10
A = 3000b^t
A = 3000\sqrt[4]{\frac{6}{5}}^{10} = 4732.3228 = 4732

Answer = 4732



4 0
3 years ago
the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .wha
gavmur [86]

Answer:

  Rs 8500

Step-by-step explanation:

For a cost price of c, the marked price is ...

  marked = c +25%·c = 1.25c

After the 15% discount, the sale price will be ...

  s = marked -15%·marked = 0.85·marked = (0.85)(1.25c) = 1.0625c

The profit will be the difference between the sale price s and the cost c:

  p = s -c

  500 = (1.0625c) -c = 0.0625c

Then the cost is ...

  500/0.0625 = c = 8000

and the sale price is ...

  s = c +p = 8000 +500 = 8500 . . . rupees

The selling price will be Rs 8500.

8 0
2 years ago
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