Question:

Mathboat.com 4 (NC). The function f (x) and g (x) are piecewise linear functions shown below. If h(x) = f(g(x)) g(x), then hil -_ )- (4) 0 (B) 2 (C) 3 (D) 1 ( E) 4 5 (NC). Which of the folllowing is the derivative of f (x) = (cost (3x) +7)? ( A) - 24(cos' (3x) +7) (cos (3x)) ( sin (3x)) 31 (B) -36( cos* (3x) +7) (cos' (3x) ) (C)-36(cos* (3x) +7) (cos' (3x)) (sin (3x)) (D) - 8 cost (3x) + 7) ( sin ( 3x) ) (E) -24( cost (3x) +7) (sin (3x)) 17Mathboat.com 6 (NC).f (x) = 2x + sin (2x); OSxS2n What are the x-coordinates of all points on the graph off where the tangent line is horizontal? (A) { n, 27) (B) 3'3) (C) 1 317 (2' 2 ( D ) ,TI , - 2 (E) 21 37 (3'2 ) 7 (NC). Ify = cos (3x), then y' = 3 (A) (B) 3 sin (3x) (C) Isin (3x) 33 2 cos (3x) 2 cos (3x) 2 cos (3x) (D) (E) 3 sin (3x) 2 cos (3x) 2 cos (3x) 188 (N C). Using the table below, what is the derivative off(g(x)) at x =1? (A)0 (3)3 (c) 7 (D)-21 (E) _14 9 (C). In the interval 0 S x s E, What are all the values of x at which the 2 O graphs of f( x): 2tan(3x) and g(x) : 3x2 have parallel tangent lines? A) 1.01 () (B)1.,01118 (C)1.,011.85 (D)118 ( J E 1.,011.18, 1.85 J.Mathboat.com 2.6a Implicit Differentiation 1(NC). What is the slope of the tangent line to the curve (x' + y)' - 2a xy = b' at the point P(0, 1) when a = V2 and b = 1? 36 (A) -2 (B) -2 ( C) 2 (D) 1 ( E) 2 2. (NC) Which of the following is y' if xy + sec y = 8? (A) -2xy . (x2 sec y tan y) (B xy sec y tan y sec y tan y 37 (C) -2 -2xy (D)- x - sec y tan x -2xy (E) - x' + sec y tan y 3NC. For what values of x does the curve y' - x* + 2xy -18x2 =10 have vertical tangent lines? ( A) x - 5 (B) x = -2y (C) x = -y (D) x = 5, x = -5 (E) x=2y SKIP 20Mathboat.com 4(NC). Given equation y*+4y -3x sin y = 2x+1, what is-? dx 70 (A) 2+9x sin y (B) 70+ 92x sin y 38 4y' + 4-3x' cos y 4 v2 +4 -3xsin y (C)- 4y' +6-32sin y (D) 2x +5 4v' - 26sin x (E) 613 -26sin x + 2 5 (NC). The slope of the tangent to the curve yx' + y'x = 10 at (2, 1) is 39 ( A) - (B) 1 (C)1 (D)O (E)- 13 22 6 (NC). For which of the following values of x or/and y does the curve 3y2 - x2 +5x' =6 have horizontal tangent line(s)? ( A x = 0 (By = 1, x =3 C x=-1 (D) y = 1, x =3, x=0 (Ey= 0 (2-1)