let f(x)={ -1 , -2

Asked by singhamanvns12345 | 30th May, 2022, 11:34: AM

Expert Answer:

vertical line f left parenthesis x right parenthesis vertical line equals open curly brackets table attributes columnalign left end attributes row cell 1 comma space space space space space space space minus 3 less or equal than x less than 0 end cell row cell 1 minus x comma space space space 0 less or equal than x less or equal than 1 end cell row cell x minus 1 comma space space space space 1 less than x less or equal than 3 end cell end table close
f left parenthesis vertical line x vertical line right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x minus 1 comma space space space space space minus 3 less or equal than x less than 0 end cell row cell x minus 1 comma space space space space space 0 less or equal than x less or equal than 3 end cell end table close

N o w comma space g left parenthesis x right parenthesis equals vertical line f left parenthesis x right parenthesis vertical line plus f left parenthesis vertical line x vertical line right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x comma space space space space space space space space space minus 3 less or equal than x less than 0 end cell row cell 0 comma space space space space space space space space space space 0 less or equal than x less or equal than 1 end cell row cell 2 x minus 2 comma space space space 1 less than x less or equal than 3 end cell end table close
g apostrophe left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 1 comma space space space minus 3 less or equal than x less than 0 end cell row cell 0 comma space space space space 0 less or equal than x less or equal than 1 end cell row cell 2 comma space space space 1 less than x less or equal than 3 end cell end table close
Now, the graph will remain constant between 0 and 1.
g'(0-) = 1, g'(0+) = 0
g'(1-) = 0, g'(1+) = 2
So, g is not differentiable at 0 and 1.

Answered by Renu Varma | 30th May, 2022, 06:24: PM