Question

prove that the function f(x) = |x| is continuous at x=0 but not differentiable at x=0

Answer 1

Answer:

Step-by-step explanation:

For a continuous function, right hand limit and left hand limit should be equal.

For a differentiable function, right hand derivative and left hand derivative should be equal.

For modulus function,only RHL is equal to LHL at x=0

Hence,it is continuous and not differentiable.It is shown in Another concept is that when you draw the graph of |x|, you will find a break or change in slope at x=0.(Graph of modulus function is V-shaped).Hope you understood

Answer 2

Answer:

$\huge \red {ANSWER}$

For a continuous function, right hand limit and left hand limit should be equal.

for a differentable of function, right hand derivative and left hand derivative should be equal.

for modulus function, only RHL is equal to LHL at x = 0

hence, it is continuous and not differentable. it is shown in another concept is that when you draw the graph of |x| , you will find a break or change in slope at x= 0 (graph of modulus function is V shaped) .

hope it's help you

thank you .....