5.7 Optimisation Quiz

1. What is the first step in an optimisation problem?

• A. Set the derivative equal to zero
• B. Write the quantity to optimise as a function of one variable
• C. Substitute the end points
• D. Round the answer to 3 s.f.

2. A rectangle has perimeter 40 m and width $x$ m. What is its area?

• A. $x(40-x)$
• B. $x(40-2x)$
• C. $x(20+x)$
• D. $x(20-x)$

3. A profit is $P(x)=-2x^2+80x-300$. For what $x$ is the profit a maximum?

• A. $x=20$
• B. $x=40$
• C. $x=80$
• D. $x=10$

4. For $P(x)=-2x^2+80x-300$, what is the maximum profit?

• A. $300$
• B. $400$
• C. $500$
• D. $800$

5. $V'(x)=0$ gives $x=5$ and $x=15$ but the domain is $0<x<15$. What do you do?

• A. Use both values
• B. Reject $x=15$ because it is outside the domain
• C. Round $x=15$ to 14
• D. Change the domain