Thread: I'm not sure how to solve this question?

Question: At t = 55 seconds, an object moving along a straight path is 47 meters from its origin. If the velocity at that time is v(55) = −3 meters per second, use a tangent line approximation to predict the object’s position at one minute (t = 60 seconds).

So I know that the equation for a tangent line is:
T(x) = f(x) + f'(x) (x-c)

But I am not sure if that is how I solve this question as I'm trying to predict the object's position.

Any help is appreciated.

Let be the position in meters of the object at time seconds. Then, where is the initial velocity in meters per second of the object and is the initial position in meters of the object.

Let be the tangent line approximation to p(t) at t = 55. Then, . Because and , .

Evaluate .

Thank you for answering!
So to evaluate L(60)..
L(60) = p(60) + p'(60)(x - 60)
Is that correct?

Sorry, I had let in my original post. The variable shouldn't be on the left-hand side of the equation.

I meant to let .

Then, .