I don\'t know what to select for the last one or the numbers for the (t,y). If s

Question

I don't know what to select for the last one or the numbers for the (t,y). If someone could help I'd really appreciate it!

Find the exact location of all the relative and absolute extrema of the function. HINT [See Examples 1 and 2.] (Order your answers from smallest to largest t.) h(t) = 3t3-9t2 with domain [-1, +0) h has l a relative maximum at (t, y) = at (t, n-( 2,-12 h has a relative minimum h ha Select at (t, y) = a relative minimum a relative maximum an absolute minimum an absolute maximum no extremum

Explanation / Answer

h(t)=3t3-9t2

for critical points h'(t)=0

h'(t)=9t2-18t =0

9t(t -2)=0

t =0 , t= 2

h"(t)=18t-18

h"(0)=-18 <0 => relative maximum

h(0)=0

(0,0) is relative maximum

h"(2)=18>0

h(2)=24 -36=-12

(2,-12) is absolute minimum

h(-1)=-3 -9 =-12

(1,-12) is absolute minimum

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