One number is 4 times another number and their product is 64. How would that be written in equation form?

1) Let f(x)=6x+6/x. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relat

brilliants [131]

Answer:

1) increasing on (-∞,-1] ∪ [1,∞), decreasing on [-1,0) ∪ (0,1]

$x = -1$ is local maximum, $x = 1$ is local minimum

2) increasing on [1,∞), decreasing on (-∞,0) ∪ (0,1]

$x = 1$ is absolute minimum

3) increasing on (-∞,0] ∪ [8,∞), decreasing on [0,4) ∪ (4,8]

$x = 0$ is local maximum, $x = 8$ is local minimum

4) increasing on [2,∞), decreasing on (-∞,2]

$x = 2$ is absolute minimum

5) increasing on the interval (0,4/9], decreasing on the interval [4/9,∞)

$x = 0$ is local minimum, $x = 4/9$ is absolute maximum

Step-by-step explanation:

To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.

1) $f(x) = 6x + 6/x$

$f\prime(x) = 6 - 6/x^2 = 0$ and $x \neq 0$

So, the roots are $x = -1$ and $x = 1$

The function is increasing on the interval (-∞,-1] ∪ [1,∞)

The function is decreasing on the interval [-1,0) ∪ (0,1]

$x = -1$ is local maximum, $x = 1$ is local minimum.

2) $f(x)=6-4/x+2/x^2$

$f\prime(x)=4/x^2-4/x^3=0$ and $x \neq 0$

So the root is $x = 1$

The function is increasing on the interval [1,∞)

The function is decreasing on the interval (-∞,0) ∪ (0,1]

$x = 1$ is absolute minimum.

3) $f(x) = 8x^2/(x-4)$

$f\prime(x) = (8x^2-64x)/(x-4)^2=0$ and $x \neq 4$

So the roots are $x = 0$ and $x = 8$

The function is increasing on the interval (-∞,0] ∪ [8,∞)

The function is decreasing on the interval [0,4) ∪ (4,8]

$x = 0$ is local maximum, $x = 8$ is local minimum.

4) $f(x)=6(x-2)^{2/3} +4=0$

$f\prime(x) = 4/(x-2)^{1/3}$ has no solution and $x = 2$ is crtitical point.

The function is increasing on the interval [2,∞)

The function is decreasing on the interval (-∞,2]

$x = 2$ is absolute minimum.

5) $f(x)=8\sqrt x - 6x$ for $x>0$

$f\prime(x) = (4/\sqrt x)-6 = 0$

So the root is $x = 4/9$

The function is increasing on the interval (0,4/9]

The function is decreasing on the interval [4/9,∞)

$x = 0$ is local minimum, $x = 4/9$ is absolute maximum.

5 0

2 years ago

I don’t understand this so can I get help

solniwko [45]

Answer:

Your image is cut off, can you provide a better one so I can try to answer it?

Step-by-step explanation:

7 0

3 years ago

Simplify the following question x+9-10=500

Katarina [22]

Step-by-step explanation:

x+9-10=500

x-1=500

x=500+1=501

3 0

3 years ago

Read 2 more answers

HELP!!! The graph is at the top! Will mark as brainliest answer!!

Alex777 [14]

Answer:

The value of BEF = 36°

Step-by-step explanation:

Given:

Angle AED = 90°

Angle BEF = 3x°

Angle CEF = 54°

Find;

The value of BEF

Computation:

We know that;

Angle AED = Angle BEC (Vertical opposite angle)

So,

Angle AED = Angle Angle BEF + Angle CEF

90 = 3x + 54

3x = 90 - 54

3x = 36

x = 36 / 3

x = 12

The value of BEF = 3x

The value of BEF = 3(12)

The value of BEF = 36°

4 0

2 years ago

A bee flies 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for fifteen minutes. Then i

Ksenya-84 [330]

A. The equation to find the distance of the flowerbed from the hive is: $\frac{x}{20}+\frac{x}{12}+900= 1200$ , where x is the distance.

B. The flowerbed is 2250 feet far from the hive.

Explanation

Suppose, the distance of the flowerbed from the hive is $x$ feet.

The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.

As, $Time=\frac{Distance}{Speed}$

So, the time taken by the bee to reach the flowerbed $= \frac{x}{20}$ seconds and the time taken to fly back to the hive $=\frac{x}{12}$ seconds.

The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.

So, the equation will be.......

$\frac{x}{20}+\frac{x}{12}+900= 1200\\ \\ \frac{3x+5x}{60}= 300\\ \\ 8x= 60*300\\ \\ 8x=18000\\ \\ x=\frac{18000}{8}=2250$

Thus, the distance of the flowerbed from the hive is 2250 feet.

5 0

3 years ago

One number is 4 times another number and their product is 64. How would that be written in equation form?​

One number is 4 times another number and their product is 64. How would that be written in equation form?