Assume our function is exponential decay, let's say f) = 2 e 10% Use calculus methods to find the equation of the tangent line to the graph at the point (1, How can you tell without a calculator whether the tangent line is above or below the graph of the function (except at the paint x=1)? Use the tangent line to get an estimates for f(0.98) and for f(1.01) and (10) Which of those estimates is the least trustworthy? What is the reason for that? Then use 11 equally spaces points in the interval (0,2), call them X 1.0, calculate the function values0 f(x).-.f (410) and use the 11 pairs of points to find a least squares line for them. To do that you want to solve the overdetermined system of the form Az = f(x) 1 ($10)] This involves the normal equations A'Ax = ATD. Write the equations for this example and solve them Xo 03 Which slope m and y-intercept b'do you get? Show your work Now that you have two different linearizations of the same function, which one is better? Justify your dechion Calculate errors and graph your results
