Find all values c in (−1, 1) such that f '(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)c =

To find all values $c$ in the interval $(-1, 1)$ such that $f'(c) = 0$, follow these steps:

1. Break Down the Problem

   • We need to identify the function $f(x)$ to compute its derivative $f'(x)$.
   • Set the derivative equal to zero and solve for $c$ within the given interval.

2. Relevant Concepts

   • The concept of critical points where the derivative equals zero is important. This implies that the function may have local maxima or minima at those points.

3. Analysis and Detail

   • Let's assume $f(x)$ is a differentiable function whose derivative can be calculated.
   • Compute $f'(x)$.
   • Solve the equation $f'(c) = 0$ for $c$.

4. Verify and Summarize

   • Confirm if the solutions for $c$ fall within the interval $(-1, 1)$.
   • List values of $c$ if they exist; otherwise, indicate "DNE".

Final Answer

Since the function $f(x)$ was not provided, the solutions cannot be specifically calculated. Please provide the function $f(x)$ to proceed with finding the critical points.