Problem Name

Problem Description

Notes

derivative_31

The following pairs of points all define secant lines to the curve through the point (2, 4). Find the slope, of each secant line:
a. (2, 4) and (3, 9)
b. (2, 4) and (2.5, 6.25)
c. (2, 4) and (2.3, 5.29)
d. (2, 4) and (2.1, 4.41)
e. (2, 4) and (2.05, 4.20)

derivative_32

Find the slope of the secant line defined by each of the following pairs of points: a. (1, 1) and (2, 4)
b. (1.5, 2.25) and (2, 4)
c. (1.7, 2.89) and (2, 4)
d. (1.8, 3.24) and (2, 4)
e. (1.9, 3.6 1) and (2,4)
f. (1.95, 3.80) and (2, 4)

derivative_33

Find the equation of the tangent line to the curve at the point (2, 4).

derivative_34

Find the equation of the tangent line to the curve through the point (7, 49). Use this tangent line to estimate square root of (50).

derivative_35

Show that the formula for the slope of the tangent line is the same as the formula for the average speed of an object over a time interval that becomes very small.

derivative_36

Use a computer spreadsheet (such as Microsoft Excel) or a graphing calculator to draw a graph of the curve between and . What happens as you make and closer together while you increase the magnification to zoom in for a closer look at the curve?

derivative_37

Find the derivative of the following function. Then evaluate the derivative for the given value of the independent variable.
; evaluate when .

derivative_38

Find the derivative of the following function. Then evaluate the derivative for the given value of the independent variable.
; evaluate when .

derivative_39

Find the derivative of the following function. Then evaluate the derivative for the given value of the independent variable.
; evaluate when .

derivative_40

Find the derivative of the following function. Then evaluate the derivative for the given value of the independent variable.
; evaluate when .