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3 years ago

Given f'(x) = (1 − x)(4 − x), determine the intervals on which f(x) is increasing or decreasing.

Mathematics

2 answers:

Sophie [7]3 years ago

8 0

The critical points are at x = 1 and x = 4 giving you the intervals (-inf, 1), (1, 4) and (4, inf).

By substituting x values in these 3 intervals, you can see that f'(x) is positive in the first and third intervals and negative in the second interval.

This means that f(x) is increasing in the first and third intervals and decreasing in the second interval.

The answer is D.

IgorC [24]3 years ago

6 0

To the risk of sounding redundant.

notice, your critical points are 1 and 4, so you check the regions about, namely, do a first-derivative test on them, check the picture below.

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The table below represents what type of function?

Troyanec [42]

Answer:

nonlinear because the second row isn't going up by the same number

3 0

2 years ago

Richard and Teo have a combined age of 37. Richard is 4 years older than twice Teo's age. How old are Richard and Teo?

valkas [14]

Answer:

Teo is 11 years old and Richard is 26 years old.

Step-by-step explanation:

Let R be the age of Richard and T be the age of Teo.

First set up the equations:

The combined age of Teo and Richard is 37:

R+T=37

Richard is four years old than twice Teo's age:

R=2T+4

Then, solve the equations:

Substitute (2) to (1) and solve for T:

(2T+4)+T=37

3T=11

T=11

Solve for R using (2):

R=2(11)+4

R=22+4

R=26

5 0

3 years ago

Use the fraction strips to compare 2/4 and 5/8. use the drop-down menus to explain your comparison.

tia_tia [17]

Answer:

$\dfrac{4}{5}$

Step-by-step explanation:

We are given 2 fractional numbers:

$1.\ \dfrac{2}4\\2.\ \dfrac{5}8$

We have to use fraction strips to compare to the fractional numbers.

Let we are Comparing $\frac{2}{4}$ with the length of $x$ number of $\frac{1}4$ sections.

i.e.

$\dfrac{2}{4} = x \times \dfrac{1}{4}\\\Rightarrow x = \dfrac{2 \times 4}{4}\\\Rightarrow x = 2$

Let we are Comparing $\frac{5}{8}$ with the length of $y$ number of $\frac{1}8$ sections.

i.e.

$\dfrac{5}{8} = y \times \dfrac{1}{8}\\\Rightarrow y = \dfrac{5 \times 8}{8}\\\Rightarrow y = 5$

Now, let us have a look at 3rd part of question:

The sections of 2/4 is _____ the length of 5/8. Therefore, 2/4 < 5/8

Let the answer be $z$ .

So, the equation becomes:

$\dfrac{2}{4} = z \times \dfrac{5}{8}\\\Rightarrow z = \dfrac{2 \times 8}{4 \times 5}\\\Rightarrow z = \dfrac{2 \times 2}{5}\\\Rightarrow z = \dfrac{4}{5}$