Use the alternative form of the derivative to find the derivative at x = c (if it exists). (if the derivative does not exist at c, enter undefined.) h(x) = |x + 8|, c = -8

The derivative of the function does not exist.

Step-by-step explanation:

The alternative form of a derivative is given by:

Our function is defined as:

h(x)=|x+8|

i.e.  h(x)=   -(x+8) when x+8<0

           and   x+8  when x+8≥0

i.e. h(x)=  -x-8   when x<-8

      and   x+8  when x≥-8

Hence now we find the derivative of the function at c=-8

i.e. we need to find the Left hand derivative (L.H.D.) and Right hand derivative (R.H.D) of the function.

The L.H.D at a point 'a' is calculated as:

Similarly R.H.D is given by:

Now for L.H.D we have to use the function h(x) =-x-8

and for R.H.D. we have to use the function h(x)=x+8

L.H.D.

we have a=-8

=

similarly for R.H.D.

Now as L.H.D≠R.H.D.

Hence, the function is not differentiable.

a=r

d=q

c=p

b=s

hope this !