Answer: 100 sq units.
- A 80 sq units
- B 100 sq units
- C 120 sq units
- D 200 sq units
Correct answer: B. 100 sq units
Explanation: Let sides be x and 20-x (since 2x+2y=40 means x+y=20). Area A = x(20-x). dA/dx = 20-2x = 0 gives x=10=y, a square. Maximum area = 10 x 10 = 100 sq units.
The tangent at a point touches the curve with slope f'(a); the normal is the line perpendicular to the tangent at that same point, with slope -1/f'(a) - together they describe the curve's local direction and the line "straight into" the curve.
Concept context
Use derivatives to study rate of change, increasing and decreasing functions, tangents and normals, and maxima and minima, with classic optimization problems.