20. The graph below displays growth of a town's population y = P(t) over the next 3 years, where t is time in months.
a. Estimate how fast the population is increasing 5 months, and 20 months from now.
b. Graph y = P'(t).

In graphs of questions 2, 4 and 6, determine which is the f(x) function and which is the derivative?

Please see the attached document for graphs. Please explain your answer well i.e. how do you arrive at the answer/decision.

20. The rate of change in the value of the function with respect to a change in the value of x is the derivative of the function. The derivative at a point is the slope of the tangent line to the graph of y=f(x) at that point. So, to estimate the growth rate 5 and 20 months from now, we need to estimate the slopes of the tangent lines to the given graph at x=5 and x=20. The first one ...

Solution Summary

The process of analyzing the graph of a function to find its values and estimate the values of its derivative is illustrated with several examples. Examples of matching the graph f a function to the graph of its derivative are also given.

... b) Find the value of the derivative at x = 4 ... 2 QSO 510 Quantitative Analysis Differential Calculus HW Set 7. ... function P(x). b) Use Excel to graph the functions ...

... a function of x : f(x) = |x|^x Lots of analysis of grpah of f ... 1] and hitting the Derivative radio button, you will find you will get the same graph as you ...

... occurs when 8x-16=0 or x=2. So f(2)=-16 1. Find the intercepts of the graph of the ... 2. Analyze the graph of the function R(x) =x+9 x(x+18) a) What is ...

... What value of x on the graph generates the maximum area ... Numerical, Graphical, and Analytic Analysis. ... the critical number(s) of this function and find the angle ...

... Including graphs and figures in the presentation ... should recruit skilled employees, analysis the market ... 9. Find derivatives of the following functions using ...

... worksheet or Microsoft Word for your regression graphs and trend ... DIV/0! #DIV/0! Research in Apple, Inc Ratio Analysis. ... 0 0 1,911 1,911 0 0 Mutual funds 1,227 0 ...

... is continuous at x = 0. We can analyze the differentiability ...Find all maximum and minimum points of the following ... x . Using an illustration of the graphs of a ...

... from u to v . We are trying to find the longest ... From the above analysis, for any u , v ∈ G , we only ... must have diamG ≤ 2 . The book is: Graph and Digraphs ...

... It is this which distinguishes hedge funds from a spate of other ... 1. Black-Scholes options pricing model 2. Simulation analysis 3. Hedging. ... (See graphs at http ...