You decide to build a 242square foot rectangular vegetable garden. In order to protect the vegetable garden, you decide to surround your 242

ft2 vegetable garden with a mulch border. The border will be 1 ft wide on two of the parallel sides and 2 ft wide on the remaining two parallel sides.

Let w and h be the dimensions of the vegetable garden as drawn in the sketch.

(a) Write an n equation in w and h that gives the constraint. The constraint is given by the equation ___

(b) Let A denote the area of the mulch border for the vegetable garden. Describe A as a function of w ONLY.

(c) Find the domain of A(w). Write the domain using interval notation. Use commas, as needed, to separate any intervals.

(d) Find the critical point(s) of A. Use commas, as needed, to separate values

(e) What does the Second Derivative Test tell us about the nature of the critical point?

(f) What dimensions for the vegetable garden will minimize the area of the mulch border? Give EXACT VALUES.