Consider the function f(x)=4x2ex7\displaystyle {f{{\left({x}\right)}}}={4}{x}^{{2}}{e}^{{-\frac{{x}}{{7}}}}.

  1. Find the first derivative. f(x)=\displaystyle {f}'{\left({x}\right)}=  
  2. List any critical values.
  3. Identify intervals of increase.
  4. Identify intervals of decrease.
  5. Use parts a through d to identify any local maximums as ordered pairs.  
  6. Use parts a through d to identify any local minimums as ordered pairs.