- #1
h20skier
- 1
- 0
Hello All, This problem comes from #18 of section 4.3 out of stewarts 6th edition.
The Question:
Consider the following function:
f(x)= e^(-x) * sqrt(x)
What I am trying to find.
a.) Find the intervals on which f is increasing and decreasing.
b.) find any relative extrema.
c.) find the intervals of concavity.
d.) find all inflection points.
For part a. I have taken the first derivative and got. 1/2x^-(1/2) *e^-x - e^-x * sqrt (x)
after simplifying i got e^-x= 0
and 1/2 x^-1/2 - sqrt x = 0
I know i need to find these for my critical points but I am having difficulty proceeding.
for extrema i know i plug in values between my critical points to see the critcal values.
after that I know I take the 2nd derivative to find critical points for my concavity.
thanks for your help!
The Question:
Consider the following function:
f(x)= e^(-x) * sqrt(x)
What I am trying to find.
a.) Find the intervals on which f is increasing and decreasing.
b.) find any relative extrema.
c.) find the intervals of concavity.
d.) find all inflection points.
For part a. I have taken the first derivative and got. 1/2x^-(1/2) *e^-x - e^-x * sqrt (x)
after simplifying i got e^-x= 0
and 1/2 x^-1/2 - sqrt x = 0
I know i need to find these for my critical points but I am having difficulty proceeding.
for extrema i know i plug in values between my critical points to see the critcal values.
after that I know I take the 2nd derivative to find critical points for my concavity.
thanks for your help!