Chapter 4.5, Problem 15E

i.

To determine

To find: To find the $dy$ for the given function $y=x^3-3x$ .

Answer to Problem 15E

The $dy$ for the given function $y=x^3-3x$ is $dy=(3x-3)dx$ .

Explanation of Solution

Given: The function $y=x^3-3x$

Formula used: $d(x^n)=n{x}^{n-1}$

Calculation:

The given function is $y=x^3-3x$

By applying the differentiation formula,

  $\begin{array}{l}dy=d(x^3-3x)\\ dy=d(x^3)-3d(x)\\ dy=(3x-3)dx\end{array}$

Conclusion:

The $dy$ for the given function $y=x^3-3x$ is $dy=(3x-3)dx$ .

ii.

To determine

To find: The value of $dy$ for the function $y=x^3-3x$ when $x=2$ and $dx=0.05$ .

Answer to Problem 15E

The value of $dy$ for the function $y=x^3-3x$ when $x=2$ and $dx=0.05$ is $0.45$ .

Explanation of Solution

Given: The function $y=x^3-3x$

Formula used: $d(x^n)=n{x}^{n-1}$

Calculation:

The given function is $y=x^3-3x$ .

The differentiation of the function is,

  $dy=(3x-3)dx$

Applying $x=2$ and $dx=0.05$ ,

  $\begin{array}{l}dy=(3(2)-3)(0.05)\\ dy=(3(4)-3)(0.05)\\ dy=9(0.05)\\ dy=0.45\end{array}$

Conclusion:

The value of $dy$ for the function $y=x^3-3x$ when $x=2$ and $dx=0.05$ is $0.45$ .