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3 years ago

FIVE STARS AND BRAINLIEST TO CORRECT ANSWER

Mathematics

1 answer:

timama [110]3 years ago

7 0

Given, f(x) = 4/x

We have to find the derivative of it.

First we have to use property of negative exponents. We know that, 1/a = a⁻¹.

So here, f(x) = 4/x = 4x⁻¹

f'(x) = 4×(-1)×(x)⁽⁻¹⁻¹⁾

= 4×(-1)×(x)⁻²

= (-4)(x)⁻²

= -4/x²

So we have got derivative of f(x) which is f'(x) = -4/x²

Now we have to find the derivative at x = 2. To find the value at x =2, we have to plug in 2 in the place of x.

f'(2) = -4/(2)² = -4/4 = -1

We have got the required answer derivative of f(x) at x =2 is -1

So option B is correct.

You might be interested in

Given f(x) = x² - 10x + 22, what is the range of f?

adoni [48]

Answer:

[-3, ∞)

Step-by-step explanation:

There are many ways to find the range but I will use the method I find the easiest.

First, find the derivative of the function.

f(x) = x² - 10x + 22

f'(x) = 2x - 10

Once you find the derivative, set the derivative equal to 0.

2x - 10 = 0

Solve for x.

2x = 10

x = 5

Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.

f(x) = x² - 10x + 22

f(5) = 5² - 10(5) + 22

= 25 - 50 +22

= -3

Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.

This means the range is : [-3, ∞)

Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).

Hope this helped!

6 0

3 years ago

What is the answer what is q

Brrunno [24]

Q is negative two thirds which is written as -2/3

8 0

3 years ago

Read 2 more answers

25 points!! Which table shows 4 points on the line that passes through the point (–1,5) and has the same slope as the line 2x+3y

mylen [45]

It is the third one hope this helped

5 0

3 years ago

Randy needs to save $2,550 for a vacation. He has 6 months to save the money. How much money must he save each month

Vladimir79 [104]

Answer:

2550/6= 425

he has to save 425 each month

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Which of the following are examples of a geometric sequence? Select any and all that apply: may be more than one correct answer.

nevsk [136]

Answer:

( 1 , -2 , 4 , -8 , 16 , ... )

( 9 , 3 , 1 , 1/3 , 1/9 , ... )

Step-by-step explanation:

A geometric sequence has a common ratio in consecutive terms,

In sequence,

$1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....$

$\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...$

i.e.

$1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....$ is not a Geometric sequence,

1 , -2 , 3 , -4 , 5 , ...

$\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...$

i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,

In sequence,

1 , -2 , 4 , -8 , 16 , ...

$\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...$

i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,

In sequence,

0 , 1 , 0 , -1 , 0 , .....

$\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...$

i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,

In sequence,

9 , 3 , 1 , 1/3 , 1/9 , ...

$\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...$

i.e. 9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,

In sequence,

1 , 3 , 5 , 7 , 9 , ...

$\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...$

i.e. 1 , 3 , 5 , 7 , 9 , ... is not a Geometric sequence

4 0

3 years ago