Skip to main content
Ch. 3 - Derivatives
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. 3 - DerivativesProblema 3.2.29b
Capitolo 3, Problema 3.2.29b

21–30. Derivatives
b. Evaluate f'(a) for the given values of a.
f(s) = 4s³+3s; a= -3, -1

Guida verificata passo dopo passo
1
Step 1: Identify the function f(s) = 4s^3 + 3s and the values of a for which we need to evaluate the derivative, which are a = -3 and a = -1.
Step 2: Find the derivative of the function f(s) with respect to s. Use the power rule, which states that the derivative of s^n is n*s^(n-1).
Step 3: Apply the power rule to each term in the function. The derivative of 4s^3 is 12s^2, and the derivative of 3s is 3.
Step 4: Combine the derivatives to get the derivative function f'(s) = 12s^2 + 3.
Step 5: Evaluate the derivative at the given values of a. Substitute s = -3 into f'(s) to find f'(-3), and substitute s = -1 into f'(s) to find f'(-1).

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:
3m

Concetti chiave

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

Derivatives

A derivative represents the rate of change of a function with respect to its variable. It is a fundamental concept in calculus that provides information about the slope of the tangent line to the curve of the function at any given point. The derivative can be computed using various rules, such as the power rule, product rule, and quotient rule.
Video consigliato:
Percorso guidato
05:44
Derivatives

Power Rule

The power rule is a basic differentiation technique used to find the derivative of functions in the form f(s) = s^n, where n is a real number. According to this rule, the derivative f'(s) is calculated as n * s^(n-1). This rule simplifies the process of differentiation for polynomial functions, making it easier to evaluate derivatives at specific points.
Video consigliato:
5:50
Power Rules

Evaluating Derivatives at Specific Points

Evaluating the derivative at specific points involves substituting the given values into the derivative function. This process allows us to determine the instantaneous rate of change of the original function at those points. In the context of the question, we will first find the derivative of f(s) and then substitute a = -3 and a = -1 to find f'(-3) and f'(-1).
Video consigliato:
04:50
Critical Points
Pratica correlata
Domanda del libro di testo

{Use of Tech} Bungee jumper A woman attached to a bungee cord jumps from a bridge that is 30 m above a river. Her height in meters above the river t seconds after the jump is y(t) = 15(1+e^−t cos t), for t ≥ 0.

b. Use a graphing utility to determine when she is moving downward and when she is moving upward during the first 10 s.  

256
views
Domanda del libro di testo

Velocity of a car The graph shows the position s=f(t) of a car t hours after 5:00 P.M. relative to its starting point s=0,where s is measured in miles. <IMAGE>

b. At approximately what time is the car traveling the fastest? The slowest?

253
views
Domanda del libro di testo

62–65. {Use of Tech} Graphing f and f'

b. Compute and graph f'.

f(x)=e^−x tan^−1 x on [0,∞)

158
views
Domanda del libro di testo

A bug is moving along the right side of the parabola y=x² at a rate such that its distance from the origin is increasing at 1 cm/min.

b. Use the equation y=x² to find an equation relating dy/dt to dx/dt.

280
views
Domanda del libro di testo

109-112 {Use of Tech} Calculating limits The following limits are the derivatives of a composite function g at a point a.

b. Use the Chain Rule to find each limit. Verify your answer by using a calculator.

limx→2(x2−3)5−1x−2{\(\displaystyle\)\(\lim\)_{x\(\to\)2}}\(\frac{\left(x^2-3\right)^5-1}{x-2}\)

383
views
Domanda del libro di testo

Throwing a stone Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 32 ft/s from a height of 48 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is s(t) = -16t²+32t+48.

b. When does the stone reach its highest point?

184
views