Explanation Given: The general equation of parabola y = a x 2 + b x + c that passes through the point ( 1 , 4 ) Slope of tangent line at x = − 1 is 6 And, slope of tangent line at x = 5 is 2 . Calculation: Since, the parabola y = a x 2 + b x + c passes through the point ( 1 , 4 ) Substituting the point into the equation of parabola That is, 4 = a ( 1 ) 2 + b ( 1 ) + c 4 = a + b + c ------ ( 1 ) Slope of tangent line to the parabola y = a x 2 + b x + c is m = d y d x m = 2 a x + b Since, the slope of tangent line at x = − 1 is 6 That is, 6 = 2 a ( − 1 ) + b 6 = − 2 a + b ------ ( 2 ) Since, the slope of tangent line at x = 5 is 2 That is, 2 = 2 a ( 5 ) + b 2 = 10 a + b ------ ( 3 ) From equation ( 2 ) we have b = 6 + 2 a Substituting in equation ( 3 ) , That is,

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3, Problem 74E

To determine

To find:The parabola y=ax2+bx+c that passes through the point (1,4) and whose tangent lines at x=−1 and x=5 have slopes 6 and 2 respectively.

Expert Solution & Answer

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - 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