Suppose f is differentiable on
left parenthesis negative infinity comma infinity right parenthesis(−∞,∞)
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.
Suppose f is differentiable on left parenthesis negative infinity comma infinity right parenthesis(−∞,∞) and assume it h...
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