# Problem 11 From Tony Tromba, Spring 2008, Math19a, Final...

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MATH 19A, FINAL REVIEW SOLUTIONS 1. Problems from Tony Tromba Problem 1.1 (From Tony Tromba, Spring 2008, Math19a, Final Exam) . Find the derivative of the following functions. a. y = e ln( x 2 +1) b. y = cos - 1 (2 x + 1) c. y = sinh(3 x + 2) d. y = sinh - 1 x e. y = ln(1 + ln x )
b. y = cos - 1 (2 x + 1)
c. y = sinh(3 x + 2)
d. y = sinh - 1 x
Date : March 12, 2010. 1
2 MATH 19A Answer. Strait forward. dy dx = 1 1 + ln x · 1 x . Problem 1.2 (From Tony Tromba, Spring 2008, Math19a, Final Exam) . The equation x 2 + xy 2 + y 3 = 1 defines a curve in the plane. Find the slope of the tangent line at (1 , - 1).
Problem 1.3 (From Tony Tromba, Spring 2008, Math19a, Final Exam) . Find the absolute maximum and minimum values of f ( x ) = 2 x 3 + 3 x 2 - 12 x + 7 on the interval [ - 3 , 3].
Problem 1.4 (From Tony Tromba, Spring 2008, Math19a, Final Exam) . Two airplanes are flying in the same direction on parallel courses 16 miles apart one at 500 mph and the other at 450 mph. How fast is the distance between them changing when the slower plane is 12 miles ahead of the faster one?
MATH 19A 3 Figure 1. Negative writhe crossings
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