`lim_(x->-7) (h(x) - h(c))/(x-c)`
` ` `lim_(x->-7) (|x+7|)/(x+7)`
In order to evaluate the above function, both the left hand limit and right hand limit need to be evaluated.
`L.H.L. = lim_(x->-7^-) (|x+7|)/(x+7) = lim_(x->-7^-) (-(x+7))/(x+7) = -1`
` `
`R.H.L. = lim_(x->-7^+) (|x+7|)/(x+7) = lim_(x->-7^+) (x+7)/(x+7) = 1`
``Because the L.H.L. `!=` R.H.L., the limit at x=-7 does not exist, and therefore the derivative at x=-7 does not exist.
` `
`f(x)=|x+7|`
`f'(-7)=lim_(h->0)(f(-7+h)-f(-7))/h`
`f'(-7)=lim_(h->0) ((-7+h+7)-(-7+7))/h`
`f'(-7)=lim_(h->0) h/h`
Since the limit is undefined , f'(-7) is not defined.
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