sketch the graph of f and determine where f is nondifferentiable.\n f(x)=\begin{cases}-2x & \text{if }x <…

sketch the graph of f and determine where f is nondifferentiable.\n f(x)=\begin{cases}-2x & \text{if }x < 1\\-2 & \text{if }xgeq1end{cases}\na.\nb.\nc.\nd.\nwhere is the function f(x) nondifferentiable? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the function f(x) is nondifferentiable at x = \n\nb. the function f(x) is differentiable for all real numbers.

sketch the graph of f and determine where f is nondifferentiable.\n f(x)=\begin{cases}-2x & \text{if }x < 1\\-2 & \text{if }xgeq1end{cases}\na.\nb.\nc.\nd.\nwhere is the function f(x) nondifferentiable? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the function f(x) is nondifferentiable at x = \n\nb. the function f(x) is differentiable for all real numbers.

Answer

Explanation:

Step1: Analyze left - hand limit of derivative

For (x < 1), (f(x)=-2x). The derivative (f^\prime(x)=-2).

Step2: Analyze right - hand limit of derivative

For (x\geq1), (f(x)= - 2). The derivative (f^\prime(x)=0).

Step3: Check differentiability at (x = 1)

The left - hand derivative (f^\prime_{-}(1)=-2) and the right - hand derivative (f^\prime_{+}(1)=0). Since (f^\prime_{-}(1)\neq f^\prime_{+}(1)), the function is non - differentiable at (x = 1).

Answer:

A. The function (f(x)) is nondifferentiable at (x = 1)