General question

[suan123]

Is this function continuous? f(x) = absolute x

[M@gpie]

It is sure that $|x|$ is a continuous function.

[suan123]

but function which is continuous have to differentiable??????

this function can't differentiate at x=0.

งงงงงงงงงงงงงงงงงง

[M@gpie]

ข้อความเดิมเขียนโดยคุณ suan123

function which is continuous have to differentiable??????

ประโยคนี้ไม่จริงครับ ตัวอย่างก็คือ ฟังก์ชัน $|x|$ ที่คุณ suan123 ยกมานั่นเอง

[nooonuii]

A differentiable function is continuous but the converse is not true.

The fact that $f(x)=|x|$ is continuous comes from the triangle inequality
$$||x|-|y||\leq |x-y|$$