(a)

The function is  and the point is .

Apply derivative on each side with respect to .

Apply Derivative of the Natural Logarithmic Function: .

.

The slope of the tangent line  is the derivative of the function at point .

Substitute  in .

.

Point-slope form of equation .

Substitute point  and slope  in the above equation.

.

The tangent line equation is .

(b)

Graph the function   and tangent line  In same viewing window.

(c)

Verify the result using the derivative feature of the graphing utility.

(a) The tangent line is .

(b)

Graph the function  and tangent line is  in same viewing window.

(c)

Verify the result using the derivative feature of the graphing utility.

.