Question

What is the instantaneous velocity of an object with position at time t equal to `f(t)= (te^(t^2-3t),t^2-e^t)` at `t=3`?

Answer 1

`(10, 6 - e^3)`

Explanation:

`f(t)= (te^(t^2-3t),t^2-e^t)`
`f'(t)= (e^(t^2-3t) + t (2t-3) e^(t^2-3t),2t-e^t)`
`= (e^(t^2-3t) (1 + t (2t-3)),2t-e^t)`

`f'(3) = ( (1)(1 + 3(3)), 6 - e^3) = (10, 6 - e^3)`