Estimate Tangent Slope from Tabulated Data
A function \(f(x)\) is defined by its values in the table below: x f(x) 1 2 2 3 3 5 4 7 5 11 Using the central difference method, estimate the slope of the tangent line to the curve at \(x = 3\).
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, \(f'(1) \approx \frac{f(1.1)-f(0.9)}{0.2}\).
Interpreting Numerical Derivatives from Digital Graphing Data
A student uses a digital graphing tool to determine the instantaneous rate of change (derivative) of a function f(x) at x = 2. The tool displays a readout of 4.8. The graph of f(x) near x = 2 appears almost linear, suggesting that the tangent at that point is well-defined. In this question, you will: […]
Secant Approximation from Measured Data Points
Given a set of data points representing time (in seconds) and position (in meters) of a moving object, use the secant approximation method to estimate the object’s instantaneous velocity at a specific time.\n\n(a) Select two consecutive data points near the time of interest.\n\n(b) Calculate the slope (secant) between these two points as an approximation for […]