APPM 1350 Midterm: appm1350fall2016exam2_sol
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Fall 2016: (28 pts, 7 pts each) the following four problems are not related. Be sure to simplify your answers. (a) let f (x) = tan2( x). Solution: (5 pts) f (x) = 2 tan( x) sec2( x) (2 pts) f (1/4) = 2 tan( /4) sec2( /4) = 2 (1)(cid:16) 2(cid:17)2. = 4 (b) find the derivative of g(x) = at x = 2. x2. Solution: (5 pts) g (x) = (2 pts) g (2) = 8 (c) consider the curve ax2 + by2 = 40. 3x2 + 4: use implicit differentiation to nd dy/dx, suppose the curve has the tangent line y = 2 + 2 constants a and b. 9 (x + 1) at the point ( 1, 2). Find the: (3 pts) 2ax + 2by , (4 pts) the point ( 1, 2) lies on the curve so a + 4b = 40. The tangent slope at ( 1, 2) is y =
