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Ch. 3 - Derivatives
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 3 - Derivatives문제 3.2.29b
3장, 문제 3.2.29b

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

검증된 단계별 안내
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).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
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가이드 코스
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.
추천 영상:
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).
추천 영상:
04:50
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