Check if the function (f(x) = |x|) is differentiable over the interval ([-2,2]).

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Accepted Answer

Step:1 ：First, we find the derivative of the function. The derivative of (f(x) = |x|) is (f&#x27;(x) = x/|x|) for (x neq 0).Step:2 ：Then, we check the derivative at the endpoints of the interval. At (x = -2), (f&#x27;(-2) = -1); at (x = 2), (f&#x27;(2) = 1).Step:3 ：Finally, we check the derivative at (x = 0), which is the point where the function is not defined. Since the derivative does not exist at (x = 0), the function is not differentiable over the interval ([-2,2]).

Answer

Step: 1 ：First, we find the derivative of the function. The derivative of (f(x) = |x|) is (f&#x27;(x) = x/|x|) for (x neq 0).Step: 2 ：Then, we check the derivative at the endpoints of the interval. At (x = -2), (f&#x27;(-2) = -1); at (x = 2), (f&#x27;(2) = 1).Step: 3 ：Finally, we check the derivative at (x = 0), which is the point where the function is not defined. Since the derivative does not exist at (x = 0), the function is not differentiable over the interval ([-2,2]).

Check if the function $f (x) = | x |$ is differentiable over the interval $[- 2, 2]$ .

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Popular Problems

Check if the function f(x)=|x| is differentiable over the interval [−2,2].

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Popular Problems

Check if the function $f (x) = | x |$ is differentiable over the interval $[- 2, 2]$ .