6568 You are asked in these exercises to determine whether a piecewise-defined function
Chapter 2, Problem 67(choose chapter or problem)
You are asked in these exercises to determine whether a piecewise-defined function f is differentiable at a value \(x=x_{0}\), where f is defined by different formulas on different sides of \(x_{0}\). You may use without proof the following result, which is a consequence of the Mean-Value Theorem (discussed in Section 4.8). Theorem. Let f be continuous at \(x_{0}\) and suppose that \(\lim _{x \rightarrow x_{0}} f^{\prime}(x)\) exists. Then f is differentiable at \(x_{0}\), and \(f^{\prime}\left(x_{0}\right)=\lim _{x \rightarrow x_{0}} f^{\prime}(x)\).
Let
\(f(x)=\left\{\begin{array}{ll} x^{2}, & x \leq 1 \\ \sqrt{x}, & x>1 \end{array}\right.\)
Determine whether f is differentiable at \(x=1\). If so, find the value of the derivative there.
Equation Transcription:
{
Text Transcription:
x=x_0
x_0
lim_x rightarrow x_0 f'(x)
f'(x_0)=lim_x rightarrow x_0 f'(x)
f(x)= {sqrt x, x > 1 x^2, x less than or equal to 1
x=9
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer