Question

f(x)=|x| is continuous and differentiable?

Answer 1

Nope...

Answer 2

It doesn't have a smooth curve.

Answer 3

Neither continuous nor differentiable?

Answer 4

it is continuous though, but not differentiable everywhere

Answer 5

- yes I'd agree with that

Answer 6

Is it differentiable and continuous at x=0?

Answer 7

continuous yes, but not differentiable, because it's at an "angle" there.

Answer 8

Oh. I see it now. but what if it was at another point? like x=1 or x=2? then it would be diff., right?

Answer 9

or not, its not a curve

Answer 10

Yes it\s differentiable elsewhere. A line is differentiable. Just think how many times you might have differentiated a linear function \(f(x) = ax+b\) to get \(\dfrac{d}{dx}f(x)=a\)

Answer 11

More generally: all polynomials are differentiable :) and a linear function is a polynomial of degree 1

Answer 12

Oh. I understand it way better now. Thanks.

Answer 13

Kind of silly. lol

Answer 14

Don't worry :P