### Home > APCALC > Chapter 7 > Lesson 7.1.1 > Problem7-11

7-11.

Find two positive numbers whose sum is $8$, such that the sum of the square of one number and the cube of the other number is a minimum. Use calculus to justify your solution.

Let $y = a^2 + b^3$
Use the fact that $a + b = 8$ to rewrite $y$ with only one variable.

Optimize! Find $y^\prime$ and set it equal to $0$.

Be sure to answer the question completely. In other words: What is $a$? What is $b$?