MATH 1230 Midterm: Math 124.02 Brown Test3 2
Document Summary
A function is continuous and di erentiable, and has values given in the following table. Fill in the table with approximate values of h (t) t. To approximate the derivative of a function you need to remember that the derivative function outputs the slope of the tangent line at a point on the graph. So, to approximate the derivative you approximate the slope of the tangent line. To approximate the slope of the tangent line nd the slope of the secant line (sometimes these lines are called chords) connecting two points on the graph of the function. Doing this for the rst two points we have that: h (1) . Now, to approximate the derivative at 1. 2 we can do it two di erent ways. h (1. 2) . Now, this is crucial, the two above approximations to the derivative can be improved by averaging the two results. Therefore, the best approximation to the derivative is given by: h (1. 2) . 75.
