Answer
(a) A = 10
(b) $A(x) = x^2+x-2$
(c) $A'(x) = 2x+1$
The derivative of $A(x)$ has the same form as $~~y = 2t+1~~$ in part a.
Work Step by Step
(a) The area consists of a triangle located above a rectangle. The total area is the sum of each part:
$A = \frac{1}{2}(2)(4)+(3)(2) = 4+6 = 10$
(b) The area consists of a triangle located above a rectangle. The total area is the sum of each part:
$A(x) = \frac{1}{2}(x-1)(2x+1-3)+(3)(x-1)$
$A(x) = \frac{1}{2}(x-1)(2x-2)+(3)(x-1)$
$A(x) = (x-1)(x-1)+(3)(x-1)$
$A(x) = (x^2-2x+1)+(3x-3)$
$A(x) = x^2+x-2$
(c) $A(x) = x^2+x-2$
$A'(x) = 2x+1$
The derivative of $A(x)$ has the same form as $~~y = 2t+1~~$ in part a.
