Suppose f is differentiable on

left parenthesis negative infinity comma infinity right parenthesis(−[infinity],[infinity])

and assume it has a local extreme value at the point

x equals 1x=1

where

f left parenthesis 1 right parenthesis equals 0f(1)=0.

Let

g left parenthesis x right parenthesis equals xf left parenthesis x right parenthesis plus 4g(x)=xf(x)+4

and let

h left parenthesis x right parenthesis equals xf left parenthesis x right parenthesis plus x plus 4h(x)=xf(x)+x+4

for all values of x.

a. Evaluate

g left parenthesis 1 right parenthesisg(1),

h left parenthesis 1 right parenthesish(1),

g prime left parenthesis 1 right parenthesisg′(1),

and

h prime left parenthesis 1 right parenthesish′(1).

b. Does either g or h have a local extreme value at

xequals=11?

Explain.