Function Notation

Question

As a mental arithmetic exercise, a teacher asked her students to think of a number, triple it, and subtract the resulting number from 24. Finally, they were asked to multiply the resulting difference by the number they first thought of.

 

Use function notation to express the final answer in terms of the original number. I solved this one which is f(x)=(24-3x)x.

 

I need help to determine the maximum result possible. I want to know how to do it step by step.

Answer 1

f(x) = (24 - 3x)x

f(x) = 24x - 3x²

f(x) = -3x² + 24x

f(x) = -3(x³ - 8x)

f(x) = -3(x² - 8x + 16) + 48

f(x) = -3(x - 4)² + 48

 

The maximum is 48 and occurs when x = 4.