abondantQ

2021-01-22

The table shows some values of the derivative of an unknown function f.Complete the table by finding the derivative of each transformation of f, it possible

a)$g(x)=f(x)\text{}-\text{}2$

b)$h(x)=2f(x)$

c)$r(x)=f(-3x)$

a)

b)

c)

ottcomn

Skilled2021-01-23Added 97 answers

Step 1

The derivative properties:

$\frac{d}{dx}(f(x)\text{}-\text{}a)={f}^{\prime}(x)$

$\frac{d}{dx}(af(x))=a{f}^{\prime}(x)$

calculate the derivative of$g(x)=f(x)\text{}-\text{}2$ with respect to x as follows

${g}^{\prime}(x)=\frac{d}{dx}(f(x)\text{}-\text{}2)$

$={f}^{\prime}(x)$

Step 2

Now calculate the derivative of$h(x)=2f(x)$ with respect to x as follows

${h}^{\prime}(x)=\frac{d}{dx}=(2f(x))$

$=2{f}^{\prime}(x)$

$\therefore {h}^{\prime}(x)=2{f}^{\prime}(x)$

Step 3

Now calculate the derivative of$r(x)=f(-3x)$ with respect to x as follows

${r}^{\prime}(x)=\frac{d}{dx}=f(-3x)$

$=\text{}-3{f}^{\prime}(-3x)$

As${r}^{\prime}(x)=\text{}-3{f}^{\prime}(-3x),$ compute the the value of

$-3{f}^{\prime}(-3x)$

${r}^{\prime}(-2)=3{f}^{\prime}[-3\text{}(2)]$

$=-3{f}^{\prime}(6)$

Here${r}^{\prime}(-2)=\text{}-3{f}^{\prime}(6)$ cannot be computed the values

of${f}^{\prime}(6)$ is not known.

${r}^{\prime}(-1)=\text{}-3{f}^{\prime}[-3\text{}(-1)]$

$=\text{}-3{f}^{\prime}(3)$

$=\text{}-3(-5)$

$=15$

${r}^{\prime}(0)=\text{}-3{f}^{\prime}[-3\text{}(0)]$

$=-3(-\frac{1}{3})$

$=1$

And${r}^{\prime}(1)=\text{}-3f[-3\text{}(1)]$

$=\text{}-3{f}^{\prime}(-3)$

Hense$-3{f}^{\prime}(-3)$ can not be compluted.

The derivative properties:

calculate the derivative of

Step 2

Now calculate the derivative of

Step 3

Now calculate the derivative of

As

Here

of

And

Hense

alenahelenash

Expert2023-05-13Added 556 answers

xleb123

Skilled2023-05-13Added 181 answers

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1)?

How to expand and simplify $2(3x+4)-3(4x-5)$?

Find an equation equivalent to ${x}^{2}-{y}^{2}=4$ in polar coordinates.

How to graph $r=5\mathrm{sin}\theta$?

How to find the length of a curve in calculus?

When two straight lines are parallel their slopes are equal.

A)True;

B)FalseIntegration of 1/sinx-sin2x dx

Converting percentage into a decimal. $8.5\%$

Arrange the following in the correct order of increasing density.

Air

Oil

Water

BrickWhat is the exact length of the spiraling polar curve $r=5{e}^{2\theta}$ from 0 to $2\pi$?

What is $\frac{\sqrt{7}}{\sqrt{11}}$ in simplest radical form?

What is the slope of the tangent line of $r=-2\mathrm{sin}\left(3\theta \right)-12\mathrm{cos}\left(\frac{\theta}{2}\right)$ at $\theta =\frac{-\pi}{3}$?

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Use the summation formulas to rewrite the expression $\Sigma \frac{2i+1}{{n}^{2}}$ as i=1 to n without the summation notation and then use the result to find the sum for n=10, 100, 1000, and 10000.

How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]?