Question

Examine the differentiability of
f(x) = x [x] , if 0 <= x < 2
and (x-1) x , if 2 <= x < 3

at x=2

Answer 1

[x] is a grea
test integer function

Answer 2

try to plot the graph.

Answer 3

pls explain how to find i dont know

Answer 4

okay..
for x belongs to [0,1), what is [x]?

Answer 5

see the definition of a greatest integer function states like this
[x] = 0, if 0 <= x <1
[x] = 1 if 1 <= x < 2
[x] = 2 if 2 <= x < 3
etc etc

Answer 6

good, then
for 0<=x<1, [x]=0,
f(x)=x[x]
for 0<=x<1, f(x)=x(0)=0.
f(x)=0 when x belongs to [0,1).
can you try out for f(x) when x belongs to [1,2)?

Answer 7

f(x) = 1 when x belongs to 1 and not 0
f(x) = 1 when x ranges from 1 to 2 but not equal to 2

Answer 8

when x=2 , the second expression holds good

Answer 9

f(x)=x when x ranges from [1,2).

Answer 10

sorry i didnt understand ur point here

Answer 11

[x]=1 when x is [1,2).
but our function is not only [x].
f(x)= the product of x and [x].
for the whole x in [1,2), [x]=1.
f(x)=x.[x]=x.(1)=x.
thus, in the interval x belongs to [1,2), f(x)=x.
and for x belonging to [2,3), f(x)=x^2-x.
if we plot the graph