Combinethecriticalpoint(s):x=0withthedomain
f(x)=e−7x2
f′(x)=−14xe−7x2
−14xe−7x2=0
x=0
Thefunctionmonotoneintervalsare: −∞<x<0 , 0<x<∞
Summaryofthemonotoneintervalsbehavior :
1) −∞<x<0⇒increasing⇒+
2) 0<x<∞ ⇒decreasing⇒−
3) x=0⇒max⇒0
Plugtheextremepointx=0intoe−7x2⇒y=1
maximum(0,1)
\mathrm{If\:}f\:''\left(x\right)>0\mathrm{\:then\:}f\left(x\right)\mathrm{\:concave\:upwards.}
\mathrm{If\:}f\:''\left(x\right)<0\mathrm{\:then\:}f\left(x\right)\mathrm{\:concave\:downwards.}
f′′(x)=0
x=(−1414,e1)
and at
x=(1414,e1)
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