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

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Answer 1 · 2017-12-23T08:47:58

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

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:

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

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