Chapter 11.3, Problem 34E

To determine

To find: the derivative of the given function

Answer to Problem 34E

The derivative of the given function is $f^{\prime }(x)=0$

Explanation of Solution

Given:

  $f\left(x\right)=-1$

Calculation:

Remember that the derivative of the function $f$ is given by

  $f^{\prime }(x)=\underset{h\to 0}{\lim }\frac{f(x+h)-f(x)}{h}$

This is a constant function, so it takes the value -1 regardless of the value of x. Therefore, to find the derivative of this function,

  $\begin{array}{l}{f}^{\prime }(x)=\underset{h\to 0}{\lim }\frac{-1-\left(-1\right)}{h}\\ =\underset{h\to 0}{\lim }0\\ =0\end{array}$

  $f^{\prime }(x)=0$

Conclusion:

Therefore, the derivative of the given function is $f^{\prime }(x)=0$