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What is the instantaneous velocity of an object moving in accordance to # f(t)= (t^3-t^2-3,e^(2t)) # at # t=6 #?

1 Answer

Dec 23, 2017

#f'(6)=(96,2e^12)#

Explanation:

Find #f'(t)# component-by-component:

#f'(t)=(d/dt(t^3-t^2-3),d/dt(e^(2t)))#
#f'(t)=(3t^2-2t,2e^(2t))#

Find #f'(6)# by direct substitution:

#f'(6)=(3(36)-12,2e^12) = (96,2e^12)#

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