2-5 Maximum and minimum applications
Point 5 of 11 — Unit 2: The Quadratic, Polynomial and Rational Functions and Their OperationsQuestion bank: 0 questions (0 with pictures)
05 2-5 Maximum and minimum applications
- A quantity modelled by a quadratic reaches its extremum at the vertex, i.e. at x = −b/(2a); the extremum value is k.
- Fenced area: with a fixed perimeter the area A(x) is quadratic in x and maximal at the vertex — the answer is always a square.
- Profit: revenue minus cost is quadratic; the maximum profit is the vertex value, and break-even points are its zeros.
- Projectile height: h(t) = −16t² + v₀t + h₀ opens downward, so the vertex gives the greatest height and its time.
- Reject any value of the variable that the situation forbids (negative time, negative price).
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