Chapter 5.7, Problem 4E

To determine

To find: the order difference when $g\left(x\right)=x^4$ to be constant.

Answer to Problem 4E

The order difference will be $5$ .

Explanation of Solution

Given information:

The function mentioned is $g\left(x\right)=x^4$ .

Formula:

For order difference we have to differentiate unless it will be zero.

Calculation:

Consider the function $g\left(x\right)=x^4$ .

Recall that for order difference we have to differentiate unless it will be zero.

Therefore we will differentiate $g\left(x\right)=x^4$ .

  $g\left(x\right)=x^4\Rightarrow g\text{'}\left(x\right)=4x^3\Rightarrow g\text{'}\text{'}\left(x\right)=12x^2\Rightarrow g\text{'}\text{'}\text{'}\left(x\right)=24x\Rightarrow g^{\text{'}\text{'}\text{'}\text{'}}\left(x\right)=24\Rightarrow g^{\text{'}\text{'}\text{'}\text{'}\text{'}}=0.$

Therefore the order difference of $g\left(x\right)=x^4$ will be $5$ .