## [answered] Calculus Writing Assignment: Tangent Line Approximation Eac

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

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).

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