9514 1404 393
Answer:
54 square units
Step-by-step explanation:
One way to find the area is to divide the figure into 3 parts using a horizontal line at y=3.
The trapezoid below the line has bases 9 and 7, and height 6, so an area of ...
A = (1/2)(b1 +b2)h
A = (1/2)(9 +7)(6) = 48 . . . . square units
The left triangle above the line has a base of 3 and a height of 2, so an area of ...
A = (1/2)bh
A = (1/2)(3)(2) = 3 . . . . square units
The right triangle above the line has a base of 6 and a height of 1, so an area of ...
A = (1/2)(6)(1) = 3 . . . . square units
Then the total area is ...
figure area = trapezoid area + left triangle area + right triangle area
figure area = (48 + 3 + 3) square units = 54 square units
. Our derivative, then, is 
.