The Fifth Gate
After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's directions to you. “The passcode for this gate is the number found by first entering m′(−1)
and then entering n′(5)
using the definitions below.” What values do you provide to your computer?

f(x)=(x8−2x)

g(x)=(x2+4x−44)

h(x)=2x−9

m(x)=f(x)⋅g(x)

n(x)=g(x)h(x)



m′(−1)=

Preview Change entry mode
n′(5)=




Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.