MATH 130 Midterm: MATH130_BOYLE-M_FALL2014_0101_MID_SOL_3

• School: University of Maryland
• Department: Mathematics
• Course: MATH 130
• Professor: All

Document Summary

Math 130 fall 2014 boyle exam 3 solutions: (12 points) (a) (10 pts) let s(x) = 8 ln(7x) 3x de ne a satisfaction function for x in. Find the value of x at which s achieves a maximum. S (x) = 8/x 3 equals zero at x = 8/3. S achieves a maximum at x = 8/3. (b) (2 pts) brie y explain how you know the maximum is achieved at this x. S (x) is positive on [2, 8/3) and is negative on (8/3, 5], so s is increasing on. [2, 8/3) and decreasing on (8/3, 5]: (13 points) (a) (9 pts) find the equation of the tangent line to the curve xy3 + ln(y) = x2 6 at the point (x, y) = (3, 1) . Use implicit di erentiation: di erentiate both sides with respect to x, then substitute x = 3, y = 1: (x) y3 + x(y3) + y3 + x(3y2y ) +