All categories

2 years ago

Determine the value(s) of x at which the function f(x)=x⁴-8x² +2 has a horizontal tangent.

Mathematics

1 answer:

Slav-nsk [51]2 years ago

3 0

Answer:

$4 {x}^{3} - 16x = 0 \\ 4x( {x}^{2} - 4) = 0 \\ 4x(x - 2)(x + 2) = 0 \\ x = 0or \: or - 2$

You might be interested in

F(x) = -2x + 5<br> f ( ) = 13

scZoUnD [109]

Answer:

Okay, I haven't done this a long time however I believe with this you have to solve the equation by doing substitution.

Step-by-step explanation:

so, if f (x) equals 13, you replace the x in the equation to 13.

f(x)=-2x+5

f(x)=-2(13)+5

f(x)=26+5

f(x)=31

I believe 41 would be your answer. Hope this is right and it helped!

4 0

3 years ago

If (-1, y) lies on the graph of y=2^2x then y=

zubka84 [21]

Answer:

y is 1/4 when x is -1 if I did interpret your equation right. Please see that I did.

I believe the equation to be $y=2^{2x}$ . If you meant $y=2^2x$ , please let me know.

Thanks kindly.

Step-by-step explanation:

If (-1,y) lies on the graph of $y=2^{2x}$ , then by substitution we have:

$y=2^{2\cdot -1}$ .

We just need to simplify to determine y:

$y=2^{2 \cdot -1}$

Multiply the 2 and -1:

$y=2^{-2}$

Use reciprocal rule for exponents to get rid of the negative:

$y=\frac{1}{2^2}$

$2^2$ just means $2(2)$ :

$y=\frac{1}{2(2)}$

$y=\frac{1}{4}$ .

8 0

2 years ago

The radius of a tire is 1.2 feet. How far will you travel after ten complete rotations of the tire?

Montano1993 [528]

Well you have to start of by finding the circumference of the tire, which you can do with the equation 2πr. If the radius is 1.2 feet, you just plug this into the equation to get 2.4π, which we will round to 7.5. After 10 rotations, you should've traveled approximately 75 feet

7 0

2 years ago

Read 2 more answers

the density of a certain material is such that weighs 6900 grams for every 4.5 quarts of volume express this density in pounds p

dlinn [17]

Answer:

$d=101.4\ \text{pounds}/\text{feet}^3$

Step-by-step explanation:

Given that,

Mass of material, m = 6900 grams

Volume of the material, V = 4.5 quarts

We need to find the density in pounds per cubic foot

We know that,

1 pound = 453.59 grams

⇒ 6900 grams = 15.21 pounds

Also, 1 cubic foot = 29.92 quarts

4.5 quart = 0.15 feet³

Density = mass/volume

$d=\dfrac{15.21\ \text{pounds}}{0.15\ \text{feet}^3}\\\\d=101.4\ \text{pounds}/\text{feet}^3$

Hence, the density of the material is $101.4\ \text{pounds}/\text{feet}^3$

3 0

3 years ago

Using the equation y = 3x – 5, what would the output be for an input of 4

SSSSS [86.1K]

The input is the x-coordinate and the output is the y-coordinate. If the input is 4, plug 4 into the x variable to find the output, y.

y=3(4)-5
y=12-5
y=7

The output is 7.

8 0

2 years ago

Read 2 more answers

Determine the value(s) of x at which the function f(x)=x⁴-8x² +2 has a horizontal tangent. ​

Determine the value(s) of x at which the function f(x)=x⁴-8x² +2 has a horizontal tangent.