(b) The function , .

Derivative of a function  is  at  defined as .

.

(a) 

Substitute  in above function.

The function is undefined when  the denominator is zero.

So  does not exist.

(c) .

Slope of the tangent to the curve  at the point  is .

Slope of the tangent to the curve  at  is .

This means that  has a vertical tangent line at .

(d) Graph:

Graph the function  with vertical tangent at .

(a)  does not exist.

(b) .

(c) The function has vertical tangent at .

(d)

.