Posted by **chelsea** on Wednesday, March 23, 2011 at 1:49pm.

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**, Thursday, March 24, 2011 at 1:06pm
use the product rule to calculate

q'(x)=4x3e^(-x)+x4*(-e^(-x)

= (4-x)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...

## Answer this Question

## Related Questions

- calculus - Let q(x)=(x^4)(e^-x). Calculate q'(x). Use q'(x) to determine whether...
- Calculus - In increasing order, rank: 3^ln 2, 2^3, 2^ln 3 *do not use a ...
- Geometry - 1. Explain whether the following statement is a valid definition: “A ...
- Please Help!!!!!! - Decide whether the following problem can be solved using ...
- Calculus - Let f be the function defined for x >or= to 0 with f(0)=5 and f', ...
- calculus - Find the area bounded by {y=x2−4 y=4−x2 • sketch the ...
- calculus - use the fundamental theorem to find the area under f(x)=x^2 between x...
- Calculus - Use the table of values to estimate ⌠6 ⎮ f(x)⋅dx &#...
- Math - Determine whether ~ [ ~(p v ~ q) <-> p v ~ q. Explain the method(s...
- Calculus - Evaluate integral, don't use calculator. I'll use the S as the sign ...