Question

studying the function derivable f: \[(0, + \infty)\] ....>R

\[\sqrt{3+x ^{2}} - x if 0 < x \le 1 \]

\[\frac{ 1 }{ x } +\frac{ x ^{2} }{4} if x > 1\]

Answer 1

@hartnn
@hba

Answer 2

to check whether the function is differentiable at x=1, check whether its continuous at x=1.
if its not continuous, then its not differentiable at x=1

Answer 3

know how to find whether its continuous or not ?

Answer 4

\[\lim_{x \rightarrow 1} 3 +x ^{2} - x = 3+1-1= 3\]

\[\lim_{x \rightarrow 1} 1/x + x ^{2}/4= 1/1 + 1/4 = 5\]

Answer 5

is not continuous

Answer 6

so, its not differentiable at x=1

Answer 7

is it correct?

Answer 8

yes.

Answer 9

thanks

Answer 10

how can solve