Skip to main content
Ch. 4 - Applications of the Derivative
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBriggs 3rd EditionCh. 4 - Applications of the DerivativeProblema 33
Capitolo 4, Problema 33

Graphing functions Use the guidelines of this section to make a complete graph of f.
f(x) = (x2 + 12)/(2x + 1)

Guida verificata passo dopo passo
1
Identify the domain of the function f(x) = (x^2 + 12)/(2x + 1). The denominator cannot be zero, so set 2x + 1 ≠ 0 and solve for x to find the domain.
Find the x-intercepts by setting the numerator equal to zero: x^2 + 12 = 0. Solve for x to determine if there are any real x-intercepts.
Determine the y-intercept by evaluating f(0). Substitute x = 0 into the function and simplify to find the y-intercept.
Identify any vertical asymptotes by setting the denominator equal to zero: 2x + 1 = 0. Solve for x to find the vertical asymptote.
Analyze the end behavior of the function by finding the horizontal asymptote. Compare the degrees of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, perform polynomial long division to find the slant asymptote.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
14m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Function Analysis

Function analysis involves examining the properties of a function, such as its domain, range, intercepts, and asymptotes. For the given function f(x) = (x² + 12)/(2x + 1), understanding these properties is crucial for graphing. This includes identifying where the function is defined and any points where it may not exist, such as vertical asymptotes.
Video consigliato:
Percorso guidato
06:29
Derivatives Applied To Velocity

Limits and Asymptotes

Limits help determine the behavior of a function as it approaches certain points, particularly at infinity or points of discontinuity. For rational functions like f(x), vertical asymptotes occur where the denominator equals zero, while horizontal asymptotes indicate the function's behavior as x approaches infinity. Analyzing these limits is essential for sketching the graph accurately.
Video consigliato:
03:07
Cases Where Limits Do Not Exist

Critical Points and Derivatives

Critical points are values of x where the derivative of a function is zero or undefined, indicating potential local maxima, minima, or points of inflection. To find these points for f(x), one must compute the derivative and solve for x. Understanding the behavior of the function at these points is vital for creating a complete and accurate graph.
Video consigliato:
04:50
Critical Points
Pratica correlata
Domanda del libro di testo

Evaluate and simplify y'.

y = (3t²−1 / 3t²+1)^−3

350
views
Domanda del libro di testo

Use the guidelines of this section to make a complete graph of f.

f(x) = tan⁻¹ (x²/√3)

237
views
Domanda del libro di testo

Use the guidelines given in Section 4.4 to make a complete graph of the following functions on their domains or on the given interval. Use a graphing utility to check your work.

ƒ(x) = 3x/(x² + 3)


174
views
Domanda del libro di testo

Graphing functions Use the guidelines of this section to make a complete graph of f.

f(x) = x²/(x - 2)

315
views
Domanda del libro di testo

Demand and elasticity The economic advisor of a large tire store proposes the demand function D(p) = 1800/p-40, where D(p) is the number of tires of one brand and size that can be sold in one day at a price p.

c. Find the elasticity function on the domain of the demand function.

294
views
Domanda del libro di testo

Graphing functions Use the guidelines of this section to make a complete graph of f.

f(x) = 3x/(x² - 1)

229
views