A circle, centre $O$ and radius $r \mathrm{~cm}$, has a sector $O A B$ of fixed area $10 \mathrm{~cm}^{2}$. Angle $A O B$ is $\theta$ radians and the perimeter of the sector is $P \mathrm{~cm}$. (iii) Determine the nature of this stationary value.

Explanation

To determine the nature of the stationary value, we need to examine the second derivative of $P$ with respect to $r$. If the second derivative is positive, then the stationary value is a minimum. If the second derivative is negative, then the stationary value is a maximum. If the second derivative is zero, then the stationary value is an inflection point. In this case, the second derivative is positive, so the stationary value is a minimum.

A circle, centre $O$ and radius $r \mathrm{~cm}$, has a sector $O A B$ of fixed area $10 \mathrm{~cm}^{2}$. Angle $A O B$ is $\theta$ radians and the perimeter of the sector is $P \mathrm{~cm}$. (iii) Determine the nature of this stationary value.

Explanation

⬆ Related Topic

📘 Syllabus

📝 Practice Questions

🤖 Practice with AI

📚 Related Concepts