Question

Consider the equation below. (Round the answers to three decimal places. If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)
f(x) = 9 sqrt(xe*^(-x)

(a) Find the interval on which f is increasing.
( , )

Find the interval on which f is decreasing.
( , )

(b) Find the local maximum value of f.


(c) Find the inflection point.
( , )

Find the interval on which f is concave up.
( , )

Find the interval on which f is concave down.(,)

Answer 1

a) 1) take the derivative set it equal to zero and you will get critical pts
2)draw a number line and pick a point to the left and right of critical points
3) plug the selected points back into the derivative and if you get a positive number write down plus and if negative write down negative over selected points. If it's going from negative to positive then it's a local minimum and decreasing on interval
(-infinity, critical point being test)
and other way around for max..

B) take the second derivative and set it equal to zero it will give you inflection pts and do the same thing again except that if it goes from - to + it will be concave up and other way around for concave down