Calculus Writing Assignment: Tangent Line Approximation Each problem is worth 5 points. Total Points: 50 Answer each of the following questions. Make sure to show your work. 1) Find an equation to the line tangent to y = (x - 3) 2 at x = 0. 2) Suppose the graph of f (x) and the graph of its derivative f (x) are shown below. Find an equation to the line tangent to y = f (x) at x = 1. 3) Suppose g(x) is a differentiable function such that g(-4) = 0 and g(-4) = 3. Find an equation to the line tangent to y = g(x) at x = -4. 4) Find an equation to the line tangent to y = 5 + |x - 2| at the coordinate (2, 5). 1 5) Find an equation to the line tangent to y = (x + 3) at x = -3. 3 6) Suppose f (x) is a differentiable function such that f (1) = 7 and f (1) = 2. Use a tangent line approximation to estimate f (0.8). 7) Use a tangent line approximation with the function g( x) = x to estimate 9.2 . 8) The table below gives specific values for a differentiable function h(t). Use this information to write an equation for the tangent line to the graph of h(t) at t = 9. 0 5 9 14 20 t h(t) 86 77 64 59 52 9) The table below gives specific values for a differentiable function p(x). Perform a tangent line approximation to estimate the y-intercept in the graph of y = p(x). Show the calculations that lead to your answer. 1 3 4 6 9 x p(x) 0.4 0.5 0.7 1.1 1.8 10) At t = 55 seconds, an object moving along a straight path is 47 meters from its origin. If the velocity at that time is v(55) = 3 meters per second, use a tangent line approximation to predict the object's position at one minute (t = 60 seconds)