Quiz Review
2.1
Points (3,27) and Q(x,y) are on the graph of the function f(x) = x3 .
Part A: Complete the table with the appropriate values: y-coordinate of Q, the point Q(x,y), and m the slope of the secant line passing through the points P and Q. Round your answer to eight significant digits.
x | y | Q(x,y) | Work msec | msec |
3.1 | | | | |
3.01 | | | | |
3.001 | | | | |
3.0001 | | | | |
Part B: Use the values in the right column of the table to guess the value of the slope of the line tangent to f at x = 3.
Part C: Use the value in Part B to find the equation of the tangent line at point P. Graph f(x) and the tangent line.
Points (3,27) and Q(x,y) are on the graph of the function f(x) = x3 .
Part A: Complete the table with the appropriate values: y-coordinate of Q, the point Q(x,y), and m the slope of the secant line passing through the points P and Q. Round your answer to eight significant digits.
x | y | Q(x,y) | Work msec | msec |
3.1 | 29.791 | (3.1, 29.791) | 29.791 - 27 / 3.1 - 3 | 27.91 |
3.01 | 27.270901 | (3.01, 27.270901) | 27.270901 - 27 / 3.01 - 3 | 27.0901 |
3.001 | 27.027009 | (3.001, 27.027009) | 27.027009 - 27 / 3.001 - 3 | 27.009001 |
3.0001 | 27.002700 | (3.00001, 27.002700) | 27.002700 - 27 / 3.0001 - 3 | 27.0009 |
Part B: Use the values in the right column of the table to guess the value of the slope of the line tangent to f at x = 3. 27
Part C: Use the value in Part B to find the equation of the tangent line at point P. Graph f(x) and the tangent line. y = 27x - 54
Graph of the function & its tangent line.
(3,27)
Graph of the function & its tangent line.
A zoomed out image
(3,27)
Consider the function f(x) = |x|.
Part A Sketch the graph of f over the interval [-2,4] and shade the region above the x-axis.
Part B Approximate the area between the x-axis and the graph of f over the interval [-2,4] using rectangles. Use the above the line approximation. Use blocks that are a width of 1 unit.
Approximate the area between the x-axis and the graph of f over the interval [-2,4] using rectangles. Use the above the line approximation. Use geometry to find the exact answer.
Approximate the area between the x-axis and the graph of f over the interval [-2,4] using rectangles. Use the above the line approximation. Use geometry to find the exact answer.
(1)(2) + (1)(1) + (1)(1) + (1)(2)+ (1)(3) + (1)(4) = 13 unit 2
The End