Question

examine the differentiability of the function
f(x)=x^2+2 at x=2

Answer 1

limit of f(x) at x=2 exists and function is continuous so f(x) is differentiable at x=2

Answer 2

it is differentiable at x=2
f\(x)=2x

Answer 3

f'(x)=2x
f'(2)=4

Answer 4

it is polynomial and polynomials are always continuous and (so limit exits) so it means this is differentiable at x=2
f'(x)=2x
f'(2)=2(2)=4

Answer 5

but who i know if differentible or not there is some method to prove

Answer 6

yes there is for example f(x)=|x| is not differentiable at x=0 and the function
f(x)=x^(2/3) is not differentiable at x=0 because take its derivative
f'(x)=2/3/(x^1/3) if i put x=0 then the function gets undefined
if limit exists then most probably derivative exists

Answer 7

a function is differentiable if the limit at that point from left hand and right hand is same and exists.

Answer 8

thx sami

Answer 9

i think i want to solve by ur way @munish

Answer 10

a differentiable function is a function whose derivative exists at each point in its domain.
if x0 is a point in the domain of a function ƒ, then ƒ is said to be differentiable at x0 if the derivative ƒ′(x0) is defined. This means that the graph of ƒ has a non-vertical tangent line at the point (x0, ƒ(x0)), and therefore cannot have a break, bend, or cusp at this point.
and rest is same as @sami-21 told

Answer 11

okay thank u @annas and @sami-21

Answer 12

as i said no thanks to friends friends are for help :)