Question

Show that the function f(x) = |x − 2| is continuous everywhere but not differentiable at x = 2.sketch the graph.

Answer 1

Step-by-step explanation:

for being continuous, the function should be defined everywhere means, f(x) should have a value for every X.

From graph, the curve should not break anywhere then it is continuous.

If slope of curve is not defined anywhere then it is said to be not differentiable at that point.

that is why every discontinuous function is non differentiable too.

Refer the picture for Graph.

If you see in graph, the slope at x=2 is not a finite value or not defined.