Hello All, This problem comes from #18 of section 4.3 out of stewarts 6th edition.(adsbygoogle = window.adsbygoogle || []).push({});

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!!

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# How derivatives affect graphs homework help

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