I am working on a question with the following data
x(t) represents the distance traveled by an object at a time t in second.
I was able to determine the interpolating polynomial using Newtons backward differences formula given the polynomial. The question then asked to determine the values of t $\in$ [0,8] for which the velocity of the object exceeds 25 metres per second.
My thinking is if i differentiate the function it would represent the change in distance with respect to time and then solving the equation would allow me to find the maximum and minimum values for the function but how does it help me determine the the range of values which is required? Can anyone guide me to the solution.