교과서 질문
Vertical tangent lines
b. Does the curve have any horizontal tangent lines? Explain.
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Ch. 3 - Derivatives
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
3장, 문제 3.2.20b
Use the graph of g in the figure to do the following. <IMAGE>
b. Find the values of x in (-2,2) at which g is not differentiable.
검증된 단계별 안내1
Step 1: Understand the concept of differentiability. A function is differentiable at a point if it has a defined derivative at that point, which means the function must be continuous and smooth (no sharp corners or cusps) at that point.
Step 2: Examine the graph of the function g(x) over the interval (-2, 2). Look for points where the graph has sharp corners, cusps, or vertical tangents, as these are common places where a function is not differentiable.
Step 3: Identify any points of discontinuity within the interval (-2, 2). A function is not differentiable at any point where it is not continuous.
Step 4: Check for any vertical tangents within the interval. A vertical tangent occurs when the slope of the tangent line is undefined, which means the derivative does not exist at that point.
Step 5: List all the x-values within the interval (-2, 2) where the function g(x) is not differentiable based on the observations from the graph.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
6m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Differentiability
A function is differentiable at a point if it has a defined derivative there, meaning the function must be continuous and have a well-defined tangent line at that point. If a function has a sharp corner, cusp, or vertical tangent, it is not differentiable at that point, even if it is continuous.
추천 영상:
가이드 코스
05:53
Finding Differentials
Continuity
A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. For differentiability, continuity is a necessary condition; however, continuity alone does not guarantee differentiability.
추천 영상:
05:34Intro to Continuity
Critical Points
Critical points are values of x where the derivative of a function is either zero or undefined. These points are essential for analyzing the behavior of the function, including identifying where it may not be differentiable, such as at corners or discontinuities.
추천 영상:
04:50Critical Points
관련 실천
교과서 질문
60–62. {Use of Tech} Multiple tangent lines Complete the following steps. <IMAGE>
b. Graph the tangent lines on the given graph.
4x³ =y²(4−x); x=2 (cissoid of Diocles)
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교과서 질문
31–32. Velocity functions A projectile is fired vertically upward into the air, and its position (in feet) above the ground after t seconds is given by the function s(t).
b. Determine the instantaneous velocity of the projectile at t=1 and t = 2 seconds.
s(t)= −16t²+100t
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교과서 질문
21–30. Derivatives
b. Evaluate f'(a) for the given values of a.
f(t) = 1/√t; a=9, 1/4
361
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교과서 질문
Explain why or why not Determine whether the following statements are true and give an explanation or counter example.
b. d²/dx² (sin x) = sin x.
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교과서 질문
Derivatives and tangent lines
b. Determine an equation of the line tangent to the graph of f at the point (a,f(a)) for the given value of a.
f(x) = 1/3x-1; a= 2
196
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