I have been teaching over 20 years. My experience covers many levels and topics with most time spent in the middle/high school setting. Classes I've taught in this setting include 6th, 7th and 8th grade math, Prealgebra, Algebra 1 & 2, Geometry, Precalculus, AP Calculus and Statistics.I have also taught developmental mathematics at Cleveland State Unviersity. Other classes as CSU included Quantitative Literacy and Precalculus.
For the function $ f $ graphed in Exercise 18:
(a) Estimate the value of $ f'(50) $.(b) Is $ f'(10) > f'(30) $?(c) Is $ f'(60) > \dfrac{f(80) - f(40)}{80 - 40} $? Explain.
A roast turkey is taken from an oven when its temperature has reached $ 185^{\circ}F $ and is placed on a table in a room where the temperature is $ 75^{\circ}F $. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour.
Suppose that 10000 dollars is deposited into a savings account earning an interest rate of 8% compounded yearly. How long will it take for this investment to double in value?
Suppose that 7000 dollars is deposited into a savings account earning an interest rate of 9.1% compounded continuously. How long will it take for this investment to be worth 9500 dollars?
The number $ N $ of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of October 1 are given.)
(a) Find the average rate of growth (i) from 2006 to 2008 (ii) from 2008 to 2010In each case, include the units. What can you conclude?
(b) Estimate the instantaneous rate of growth in 2010 by taking the average of two average rates of change. What are its units?
(c) Estimate the instantaneous rate of growth in 2010 by measuring the slope of a tangent.
The graph of a function $ f $ is given. Estimate $ \displaystyle \int^{10}_0 f(x)\, dx $ using five subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints.
Jessica and Matthew are running toward the point $P$ along the straight paths that make a fixed angle of $\theta$ (Figure 3$) .$ Suppose that Matthew runs with velocity $v_{a} \mathrm{m} / \mathrm{s}$ and Jessica with velocity $v_{b} \mathrm{m} / \mathrm{s}$ . Let $f(x, y)$ be the distance from Matthew to Jessica when Matthew is $x$ meters from $P$ and Jessica is $y$ meters from $P$$$\begin{array}{l}{\text { (a) Show that } f(x, y)=\sqrt{x^{2}+y^{2}-2 x y \cos \theta}} \\ {\text { (b) Assume that } \theta=\pi / 3 \text { . Use the Chain Rule to determine the rate }} \\ {\text { at which the distance between Matthew and Jessica is changing when }} \\ {x=30, y=20, v_{a}=4 \mathrm{m} / \mathrm{s}, \text { and } v_{b}=3 \mathrm{m} / \mathrm{s} .}\end{array}$$
