Question

Which of the following function(s) is continuous and differentiable?

Answer 1

i. f(x)=\[5/\sqrt{x} \]
ii. g(x)=x\[\left| x \right|\]
iii. h(x)=\[\left\{ 7x+1 \rightarrow x \le 0 \right\}\] \[\left\{ x^2+1\rightarrow 0<x \right\}\]

Answer 2

by "differntiable" you mean "differentiable for all x"?

Answer 3

first one is not even defined for non positive values of x

Answer 4

no which one is continuous and diffrentiable.

Answer 5

second one is continuous everywhere, and differentiable everywhere except at \(x=0\)

Answer 6

okay. now do you know what they mean by differentiable?

Answer 7

differentiable means the derivative, which is a limit, exists. so for example
\[g(x)=|x|\] is differentiable for all numbers except 0, because it has a corner there and therefore the limit of the difference quotient does not exist at 0

Answer 8

i don't understand what your third function is

Answer 9

2 functions that were suppose to be under the same bracket sign. and the first one 0 greater than or equal to x and the 2nd one is greater than x. basically just finding x

Answer 10

\[f(x) = \left\{\begin{array}{rcc}
7x + 1 & \text{if} & x \leq 0 \\
x^2+1& \text{if} & x >0
\end{array}
\right.\]
like that?