Analyzing Sensor Data in Kinematics
A vehicle is equipped with a sensor that records its velocity at specific time intervals during an acceleration phase. The sensor recorded partial data as follows: – At \(t = 0\) seconds, \(v = 0\) m/s – At \(t = 2\) seconds, \(v = 12\) m/s – At \(t = 4\) seconds, \(v = 20\) […]
Part b
Construct a difference table using the values \(x=0.8, 0.9, 1.0, 1.1,\) and \(1.2\) to estimate the derivative of \(f(x)=x^3-3x+2\) at \(x=1\). Use the central difference formula, \(f'(1) \approx \frac{f(1.1)-f(0.9)}{0.2}\).