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1. Suppose that f(x) and g(x) are differentiable functions and it is known that: f(3) = 2, f'(3) = 7, g(3) = 4, and g'(3) = 1 If p(x) = f(x) · g(x) and q(x) = f(), calculate p'(3) and q' (3). g(x)

1. Suppose that f(x) and g(x) are differentiable functions and it is known that: f(3) = 2, f'(3) = 7, g(3) = 4, and g'(3) = 1 If p(x) = f(x) · g(x) and q(x) = f(), calculate p'(3) and q' (3). g(x)

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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8:09 PM Wed Mar 8 X по Q Name 오 Math130_HW6_XYZ... V OOO I (t) 11 = TIME SENSITIVE Reminders Do planner every night Math 130: Written Homework 6 Chapter 3 Sections 3.1 (Derivatives of Poly/Exp), 3.2( Derivatives of Trig) O Instructions: Please show all of your work, justify each step, and state any theorems or facts used from lectures. Do not simplify answers unless explicitly asked to do so. Section 3.1 WV 1. Suppose that f(x) and g(x) are differentiable functions and it is known that: f(3) = 2, f'(3) = 7, g(3) = 4, and g'(3) = 1 If p(x) = f(x) · g(x) and q(x) = f(), calculate p'(3) and q' (3). g(x) 2. Let y = xe. Find an equation of the tangent line to the curve at the point x = 2. 3. When a camera flashes, the intensity of light seen by the eye is given by the function: 100t et where I is measured in candles and t is measured in milliseconds. (a) Compute the average rate of change of intensity between time t = 6 milliseconds and t = 8 milliseconds. Include appropriate units and discuss the meaning of this value. (b) Compute I'(6). Include appropriate units and discuss the meaning of this value. (Hint: graph the function I(t) in Desmos. Use your graph to check if your answers to (a) and (b) make sense). Section 3.2 sin A Guided Proof: Consider the function f(x) = tan(x), and remember that tan(x) = cos a X Written hw # (2,28²) m tangent y-y₁= m(x-x; y-2e²=3e²c y-2e²=3e² +2e² +2 y= 3e³x-u 3. I(+)= 10 ( AI-I( = 10 b) I'l
Transcribed Image Text:8:09 PM Wed Mar 8 X по Q Name 오 Math130_HW6_XYZ... V OOO I (t) 11 = TIME SENSITIVE Reminders Do planner every night Math 130: Written Homework 6 Chapter 3 Sections 3.1 (Derivatives of Poly/Exp), 3.2( Derivatives of Trig) O Instructions: Please show all of your work, justify each step, and state any theorems or facts used from lectures. Do not simplify answers unless explicitly asked to do so. Section 3.1 WV 1. Suppose that f(x) and g(x) are differentiable functions and it is known that: f(3) = 2, f'(3) = 7, g(3) = 4, and g'(3) = 1 If p(x) = f(x) · g(x) and q(x) = f(), calculate p'(3) and q' (3). g(x) 2. Let y = xe. Find an equation of the tangent line to the curve at the point x = 2. 3. When a camera flashes, the intensity of light seen by the eye is given by the function: 100t et where I is measured in candles and t is measured in milliseconds. (a) Compute the average rate of change of intensity between time t = 6 milliseconds and t = 8 milliseconds. Include appropriate units and discuss the meaning of this value. (b) Compute I'(6). Include appropriate units and discuss the meaning of this value. (Hint: graph the function I(t) in Desmos. Use your graph to check if your answers to (a) and (b) make sense). Section 3.2 sin A Guided Proof: Consider the function f(x) = tan(x), and remember that tan(x) = cos a X Written hw # (2,28²) m tangent y-y₁= m(x-x; y-2e²=3e²c y-2e²=3e² +2e² +2 y= 3e³x-u 3. I(+)= 10 ( AI-I( = 10 b) I'l
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