The function represented by the following graph is

Question

The function represented by the following graph is (A) Differentiable but not continuous at x = 1 (B) Neither continuous nor differentiable at x = 1 (C) Continuous but not differentiable at x = 1 (D) Continuous and differentiable at x = 1

Tardigrade Admin · Accepted Answer

Given, graph is a function of f(x)=|x-1| It is clear from the graph that their is no break in the graph, it shows that it is continuous. Also, their a sharp edge at point A, so it is not differentiable at x=1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/008efb764f1252688e45637b9c893851-.png" />

Q. The function represented by the following graph is

Differentiable but not continuous at x = 1

Neither continuous nor differentiable at x = 1

Continuous but not differentiable at x = 1

Continuous and differentiable at x = 1

Given, graph is a function of
$f (x) = ∣ x - 1∣$
It is clear from the graph that their is no break in the graph, it shows that it is continuous.
Also, their a sharp edge at point $A$ , so it is not differentiable at $x = 1$

Q. The function represented by the following graph is

Differentiable but not continuous at x = 1

Neither continuous nor differentiable at x = 1

Continuous but not differentiable at x = 1

Continuous and differentiable at x = 1

Given, graph is a function of f(x)=∣x−1∣ It is clear from the graph that their is no break in the graph, it shows that it is continuous. Also, their a sharp edge at point A, so it is not differentiable at x=1

Given, graph is a function of
$f (x) = ∣ x - 1∣$
It is clear from the graph that their is no break in the graph, it shows that it is continuous.
Also, their a sharp edge at point $A$ , so it is not differentiable at $x = 1$