Math 130 spring 2015 boyle exam 2 solutions: no calculators or electronic devices allowed, where a calculator would be used, give your answer as an expression a calculator could evaluate. For each of the following functions, nd the formula for y . (a) (7 pts) y = 2 5x. Solution. y = 2 5x = e(ln 2)( 5x) y = (ln 2)( 5)e(ln 2)( 5x) = (5 ln 2)2 5x . (b) (7 pts) y = ln(| sin(2x)|). = 2 cot(2x) : (14 points) (a) (7 pts) given y = log10( 3x), nd the formula for y . 2x ln(10) (b) (7 pts) given y = (cos(x))/(x2 + 1), nd the formula for y . Solution. y = (x2 + 1)( sinx) (cosx)(2x) (x2 + 1)2: (14 points) Find every relative extreme value of the function f (x) = (ln x)(x2), and indi- cate which are relative maxima and which are relative minima. (remember, values are outputs. )