A car is at location f(0) = 10 miles with a velocity of f'(0) = 10 mi/min, acceleration f''(0) = 2 mi/min^2 and f'''(0) = -1 mi/min^3. Predict the location of the car at time t = 2 min.
Here is what I think needs to be done. A Taylor polynomial needs to be made using the above info. Once that is done plug in the time value and I should get the location.
Now how to interpet the info? All the functions are given with 0 as the input. So does that mean the start time of 0 or is this a Maclaurin Polynomial? I know that the dirivatives of f(x) form the coeffients of the powers of x in a Taylor/Maclaurin Polynomial.
The second dirivative of the location function is acceration but i do not know what the third dirivative is. the question says f'''(0) = -1 mi/min^3, i just don't see how this relates to finding location.
So I think the answer is something like this
P(x) = 10 + 10x + (2/2!)x + (2/2!)x^2 -(1/3!)x^3
P(2) = 32.67
i did some adding wrong but fixed it.