(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)

.