Posted by chelsea on .
Let q(x)=(x^4)(e^x). Calculate q'(x). Use q'(x) to determine whether q(5)<q(6) or q(5)>q(6) (do not use a calculator). Explain your reasoning.

calculus 
MathMate,
use the product rule to calculate
q'(x)=4x3e^(x)+x4*(e^(x)
= (4x)x^3*e^(x)
Since e^(x)>0 on ℝ, this means
that q'(x) has zeroes at x=0 and x=4 only.
q'(5)=125e^(5)<0
which demonstrates that q(x) is strictly monotonically decreasing on [4,∞) and therefore...