Question

find the derivative from the left and right f(x)=7 at x=0 ... ​

Answer 1

According to the first principle of deriative,

A derivative is simply a measure of the rate of the change

whose y=f(x)  with respect to its variable x

GIven : f1(a_)=limh→0+hf(a)−f(a−h)

=limh→0−hf(a)−f(a−h)

=limx→0+a−xf(a)−f(x)

W.K.T differntiation of an even function is odd and vice versa.

T.F.T of x is odd

then left hand derivative of f at x=0

=limh→0−−hf(a−h)−f(a)

since x is odd and x=a ,the derivative should be an even function

which should be of the form

f1(x)=limh→0−hf(x−h)−f(x)substitute x=a