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a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5) using the chain rule c) f(x) = Inx + 4e-e

a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5) using the chain rule c) f(x) = Inx + 4e-e

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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1. Find f '(x) a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5)" using the chain rule c) f(x) = Inx + 4e*- e 2. Given xy + 3x =-1; find a) f '(x) b) the equation of the tangent line at the point (-3,4) . 3. Given the price - demand equation: p + 0.025x = 25 a) Express the demand x as a function of the price p. [HINT Solve for x since x = f(p)] b) Find the clasticity of demand E (p) if E (p) = - p f '(p) f(p) 4. Find the integrals a) Í (5ex + °) dx b) § 4x(3 - 7x) dx c) [ 3x6-x f * dx 5. If the marginal Revenue of producing x units of a commodity is given by R'(x) = 400x – 0.4x and no revenue results at a zero production level, find: a) the Revenue function R(x) and b) the Revenue of producing 100 units
Transcribed Image Text:1. Find f '(x) a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5)" using the chain rule c) f(x) = Inx + 4e*- e 2. Given xy + 3x =-1; find a) f '(x) b) the equation of the tangent line at the point (-3,4) . 3. Given the price - demand equation: p + 0.025x = 25 a) Express the demand x as a function of the price p. [HINT Solve for x since x = f(p)] b) Find the clasticity of demand E (p) if E (p) = - p f '(p) f(p) 4. Find the integrals a) Í (5ex + °) dx b) § 4x(3 - 7x) dx c) [ 3x6-x f * dx 5. If the marginal Revenue of producing x units of a commodity is given by R'(x) = 400x – 0.4x and no revenue results at a zero production level, find: a) the Revenue function R(x) and b) the Revenue of producing 100 units
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