Question

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

Answer 1

`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)`