Optimization Problems — Geometric
10 tutor-authored questions for this Ontario curriculum expectation, ordered easiest to hardest — every one with a full worked solution. Work through them free, no account needed.
Sample: the first question, solved
"A rectangular garden uses 80m of fencing for all four sides. Using calculus, find the side length that maximizes the area (a square)."
📘 Worked solution
✓Let the sides be w and l with 2w+2l=80, so l=40−w. Area A(w)=w(40−w)=40w−w². A'(w)=40−2w=0 gives w=20, and by symmetry l=20 too — the enclosed square's side is w = 20 m.
And one from the hard end
"A box (open top) is made from a 20cm×20cm sheet, cutting squares of side x from each corner. Find x maximizing volume."
Solution shown after you try it in practice mode.
Work through all 10, easiest to hardest
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