### Home > CALC > Chapter 7 > Lesson 7.1.1 > Problem 7-11

7-11.

Find two positive numbers whose sum is 8, such that the sum of the square of the first and the cube of the second is a minimum. Use calculus to justify your solution. Homework Help ✎

Let *y* = *a*² + *b*³

Use the fact that *a* + *b* = 8 to rewrite *y* with only one variable.

Optimize! Find *y*' and set it equal to 0.

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