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**jkami** Find the local extreme points, concavity and inflecton points using first and second derivative test.

1. $\displaystyle h(x)=xlnx$

My answer: Local Minimim (0.37, -0.37), concave up, no infection points

2. $\displaystyle g(x)=\frac1{t}$

My answer: no extreme points, no concavity, no inflection points

3. $\displaystyle m(x)=2x+\frac1{x}$

My answer:

Local Maxium$\displaystyle (-\frac{1}{\sqrt2}, -2-\frac2{\sqrt2})$ concave down

Local Minimum$\displaystyle (\frac{1}{\sqrt2}, 2+\frac2{\sqrt2}) $ concave up

No inflection points

4. $\displaystyle w(x)=x^4-2x^2+x+1$

My answer: no extreme points, no concavity, no inflection points

5.$\displaystyle w(s)=s^2e^s$

My answer:

Local Minimum$\displaystyle (0,0)$ concave down

Local Maximum$\displaystyle (-2,\frac1{2})$ concave up

No inflection points