Find f'(x) for the following function.

Try the suggested solution, note, the principle is based on the property of logarithm and the answer is underlined with green colour.

The graph can be divided into two shapes. A rectangle and a right triangle.

The distance that the rover will cover if it completes one circuit can be computed using the Pythagorean theorem and adding the sides of the rectangle.

Rectangle:
Width = 4 - 2 = 2 meters 
Length = 11 - 2 = 9 meters

Triangle = 16 - 2 = 14 ; 14 - 2 = 12 meters  (this is the short leg)
long leg of the triangle = length of the rectangle = 9 meters.

12² + 9² = c²
144 + 81 = c² 
225 = c² 
√225 = √c²
15 = c

Point A to B = 4 - 2 = 2 meters
Point B to C = 15 meters
Point C to D = 16 - 2 = 14 meters
Point D to A = 11 - 2 = 9 meters

Total distance traveled = 2 + 15 + 14 + 9 = 40 meters.