11th Edition

ISBN: 9780136845881

Author: Sullivan

Publisher: VST

Concept explainers

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Textbook Question

Chapter 4.4, Problem 80AYU

Problems 72-75 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Find the function whose graph is the same as the graph of $y = | x |$ but shifted down 4 units.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.4, Problem 79AYU

Chapter 4.4, Problem 81AYU

Students have asked these similar questions

The OU process studied in the previous problem is a common model for interest rates. Another common model is the CIR model, which solves the SDE: dX₁ = (a = X₁) dt + σ √X+dWt, - under the condition Xoxo. We cannot solve this SDE explicitly. = (a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler scheme to simulate a trajectory of the CIR process. On a graph, represent both the trajectory of the OU process and the trajectory of the CIR process for the same Brownian path. (b) Repeat the simulation of the CIR process above M times (M large), for a large value of T, and use the result to estimate the long-term expectation and variance of the CIR process. How do they compare to the ones of the OU process? Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000. 1 (c) If you use larger values than above for the parameters, such as the ones in Problem 1, you may encounter errors when implementing the Euler scheme for CIR. Explain why.

#8 (a) Find the equation of the tangent line to y = √x+3 at x=6 (b) Find the differential dy at y = √x +3 and evaluate it for x=6 and dx = 0.3

Q.2 Q.4 Determine ffx dA where R is upper half of the circle shown below. x²+y2=1 (1,0)

Chapter 4 Solutions

EBK PEARSON ETEXT PRECALCULUS -- ACCESS

Ch. 4.1 - The intercepts of the equation 9 x 2 +4y=36 are...Ch. 4.1 - Is the expression 4 x 3 3.6 x 2 2 a polynomial?...Ch. 4.1 - To graph y= x 2 4 , you would shift the graph of...Ch. 4.1 - True or False The x-intercepts of the graph of a...Ch. 4.1 - Multiple Choice The cube function f(x)=x3 is ....Ch. 4.1 - The graph of every polynomial function is both...Ch. 4.1 - If r is a real zero of even multiplicity of a...Ch. 4.1 - The graphs of power functions of the form f(x)= x...Ch. 4.1 - If r is a solution to the equation f(x)=0 , name...Ch. 4.1 - The points at which a graph changes direction...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Problems 72-75 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find the function whose graph is the same as the graph of y = | x | but shifted down 4 units.

Solution Summary: The author explains that the function whose graph is the same as the graph of y was shifted down 4 units.

Concept explainers

Videos

Want to see the full answer?

Chapter 4 Solutions