MATH 201 - Homework 8 Reading Please read Section 1.4 of Active Calculus through Definition 1.4.2. This discussion will help you understand one of our recent big ideas: think of the derivative of a function as a function itself. Written homework 1. Let f be the function defined by / (t) = 5. a. Complete the following table, which you will use to estimate /"(1). Be very careful about rounding, especially when you calculate the last column. If you round values in the middle of your calculation, your numbers in the last column will not make sense. Keep as many decimal places as possible! h 1 +h f(1 + A) f(1 + h) - /(1) h 0.01 0:001 0.0001 0.00001 b. Judging from the numbers in the table, what is your best estimate of f(1)? C. How many decimal places in your estimate of f (1) are you confident are correct? Explain your thinking using what you see in the table. 2. Last week, you read the beginning of Section 1.3 in Active Calculus, which connected tangent lines to the graph of a function and values of the derivative of that function. A key point is Note 1 3.7. Review this part of the textbook and rewrite Note 1 3.7 In your own words in a way that makes sense to you.3. I graphed a function, /(x), in Desmos. 4. Mark the point (1, -1) on the graph of f and add the tangent line to the graph at that point. (Judge as best you can the line that just graces the graph at this point] 5. Find the equation of the tangent line that you added to the graph. Show your work. (Remember, the equation of a line has the form y = mx + bj 6. What is your best estimate for the derivative f"(1) of the function / (graphed above] at x = 17