Originally Posted by

**skeske1234** Determine the points of inflection in each graph.

Can someone check my answers below for correctness? Thanks in advance.

a) f(x)=xe^(-x)

f''(x)=e^(-x)(e^(-x) +x) ... f''(x) is incorrect

f''(x)=0 DNE

therefore no poitns of inflection ... an inflection point exists at x = 2

b) f(x)= e^x + e^(-x)

f''(x)=e^x+ e^(-x)

f''(x)= 0 DNE

therefore no points of inflection

c) f(x)= x-lnx

f''(x)=(x^2+1)/x^2 f''(x) = 1/x^2

f''(x)=undefined when x=0

therefore point of inflection is (0,0) the function itself is undefined at x = 0 ... no inflection point.

d) f(x)=x^4 + 4x^3

f''(x)=12x^2+24x

f''(x)=0 when x= -2 or x=0

therefore points of inflection are (0,0) and (-2,-16)