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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 63b
3장, 문제 63b

Let f(x) = x2 - 6x + 5.
Find the values of x for which the slope of the curve y = f(x) is 2.

검증된 단계별 안내
1
Step 1: To find the slope of the curve y = f(x), we need to find the derivative of f(x). The function given is f(x) = x^2 - 6x + 5.
Step 2: Differentiate f(x) with respect to x. The derivative, f'(x), represents the slope of the curve at any point x. Use the power rule: if f(x) = ax^n, then f'(x) = n*ax^(n-1).
Step 3: Apply the power rule to each term in f(x). The derivative of x^2 is 2x, the derivative of -6x is -6, and the derivative of a constant (5) is 0. Therefore, f'(x) = 2x - 6.
Step 4: Set the derivative equal to the given slope value. We want the slope to be 2, so set f'(x) = 2x - 6 equal to 2.
Step 5: Solve the equation 2x - 6 = 2 for x. This will give you the x-values where the slope of the curve is 2.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m

주요 개념

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

Derivative

The derivative of a function measures the rate at which the function's value changes as its input changes. It is often interpreted as the slope of the tangent line to the curve at a given point. For the function f(x) = x² - 6x + 5, finding the derivative f'(x) will allow us to determine the slope of the curve at any point x.
추천 영상:
가이드 코스
05:44
Derivatives

Slope of the Curve

The slope of the curve at a specific point is given by the value of the derivative at that point. In this problem, we are interested in finding the values of x where the slope of the curve, represented by f'(x), equals 2. This involves setting the derivative equal to 2 and solving for x.
추천 영상:
11:41
Summary of Curve Sketching

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax² + bx + c. The graph of a quadratic function is a parabola. In this case, the function f(x) = x² - 6x + 5 is a quadratic function, and understanding its properties, such as its vertex and axis of symmetry, can provide insights into its behavior and the solutions to the slope problem.
추천 영상:
6:04
Introduction to Polynomial Functions
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