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Sketch a graph of f'(x) Hint : let us say the functions I have drawn are 3 on (-o, –1]; x + on [-1, 1) U (1,2); and sin(27 x) – 2 on (2, 0). 2 x+3 Note:l do not expect you to know the derivative of sin(2nx) – 2. As such, I will just comment that the greatest slope of a tangent line on that function is 27T (that should be sufficient for a good sketch). If you've learned about derivatives before or have read ahead, you may recall I(sin(2rx)|' 2Tcos(27x) - this is an application of the chain rule and trigonometric differentiation!

Sketch a graph of f'(x) Hint : let us say the functions I have drawn are 3 on (-o, –1]; x + on [-1, 1) U (1,2); and sin(27 x) – 2 on (2, 0). 2 x+3 Note:l do not expect you to know the derivative of sin(2nx) – 2. As such, I will just comment that the greatest slope of a tangent line on that function is 27T (that should be sufficient for a good sketch). If you've learned about derivatives before or have read ahead, you may recall I(sin(2rx)|' 2Tcos(27x) - this is an application of the chain rule and trigonometric differentiation!

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Sketch a graph of \( f'(x) \)** **Hint**: Let us say the functions I have drawn are \(\frac{2}{x+3}\) on \((-\infty, -1]\); \(\frac{1}{2}x + \frac{3}{2}\) on \([-1, 1) \cup (1, 2)\); and \(\sin(2\pi x) - 2\) on \((2, \infty)\). **Note**: I do not expect you to know the derivative of \(\sin(2\pi x) - 2\). As such, I will just comment that the greatest slope of a tangent line on that function is \(2\pi\) (that should be sufficient for a good sketch). If you've learned about derivatives before or have read ahead, you may recall \([(\sin(2\pi x))'] = 2\pi \cos(2\pi x)\) - this is an application of the chain rule and trigonometric differentiation!
Transcribed Image Text:**Sketch a graph of \( f'(x) \)** **Hint**: Let us say the functions I have drawn are \(\frac{2}{x+3}\) on \((-\infty, -1]\); \(\frac{1}{2}x + \frac{3}{2}\) on \([-1, 1) \cup (1, 2)\); and \(\sin(2\pi x) - 2\) on \((2, \infty)\). **Note**: I do not expect you to know the derivative of \(\sin(2\pi x) - 2\). As such, I will just comment that the greatest slope of a tangent line on that function is \(2\pi\) (that should be sufficient for a good sketch). If you've learned about derivatives before or have read ahead, you may recall \([(\sin(2\pi x))'] = 2\pi \cos(2\pi x)\) - this is an application of the chain rule and trigonometric differentiation!
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Given function is

f(x)=2x+3(-∞,1]x2+32[-1,1)∪(1,2)sin(2πx)-2(2,∞)

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