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Consider the family of functions: f(x)= ex(3x-a)² where a and b are both positive constants such that ab<6. The first derivative for fis f'(x)= ex(3x-a)(3bx-ab+6) (a) There are exactly two critical points for f: one is positive and one is negative. Determine each. Hint: ab < 6: this may be helpful in determining which critical point is which (negative critical point) x₁ = (positive critical point) x₂ = (b) Suppose fhas critical points at x = -5 and x = 4. Determine the exact value of the constants a and b. a= b=

Consider the family of functions: f(x)= ex(3x-a)² where a and b are both positive constants such that ab<6. The first derivative for fis f'(x)= ex(3x-a)(3bx-ab+6) (a) There are exactly two critical points for f: one is positive and one is negative. Determine each. Hint: ab < 6: this may be helpful in determining which critical point is which (negative critical point) x₁ = (positive critical point) x₂ = (b) Suppose fhas critical points at x = -5 and x = 4. Determine the exact value of the constants a and b. a= b=

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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Consider the family of functions: f(x) = ex(3x-a)2 where a and b are both positive constants such that ab<6. The first derivative for fis f'(x) = x(3x-a)(3bx-ab+6). (a) There are exactly two critical points for f: one is positive and one is negative. Determine each. Hint: ab 6: this may be helpful in determining which critical point is which (negative critical point) x₁ = (positive critical point) x₂ = (b) Suppose f has critical points at x = -5 and x = 4. Determine the exact value of the constants a and b. a= b=
Transcribed Image Text:Consider the family of functions: f(x) = ex(3x-a)2 where a and b are both positive constants such that ab<6. The first derivative for fis f'(x) = x(3x-a)(3bx-ab+6). (a) There are exactly two critical points for f: one is positive and one is negative. Determine each. Hint: ab 6: this may be helpful in determining which critical point is which (negative critical point) x₁ = (positive critical point) x₂ = (b) Suppose f has critical points at x = -5 and x = 4. Determine the exact value of the constants a and b. a= b=
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