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Suppose that ( f ( x ) = ( 1 + 5 x ) e ^ { 4 x } ) . a

Suppose that \( f(x)=(1+5 x) e^{4 x}\). a. Find all critical numbers of \( f \).(If there are multiple values, enter them separated by commas. If there are no critical points, enter DNE.)\[ x=\] b. Use interval notation to indicate where \( f \) is increasing. (If there are multiple intervals, enter them separated by commas.) c. Use interval notation to indicate where \( f \) is decreasing. (If there are multiple intervals, enter them separated by commas.) d. List the x-coordinates of all local maxima of \( f \).(If there are multiple values, enter them separated by commas. If there are no local maxima, enter DNE.)\[ x=\] e. List the x -coordinates of all local minima of \( f \).(If there are multiple values, enter them separated by commas. If there are no local minima, enter DNE.)
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x=
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f. Use interval notation to indicate where \( f \) is concave up.(If there are multiple intervals, enter them separated by commas.)
g. Use interval notation to indicate where \( f \) is concave down. (If there are multiple intervals, enter them separated by commas.)
h. List the \( x \)-values of all inflection points of \( f \).(If there are multiple values, enter them separated by commas. If there are no inflection points, enter DNE.)
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x=
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Suppose that \ ( f ( x ) = ( 1 + 5 x ) e ^ { 4 x

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