1. At which of the following values of x is g(x) undefined and g'(x) is undefined? Graph of g(x) I. x =-2 II. x = 2 III. x = 3 TAY I only (B) I and II only ( II and III only DylI only - derivative 2. If f(x) = 2xsin x , then what is the slope of the tangent line to the graph of f (x) when x = ? 2 (A) 2 (B) (C) 0 (D) 2 x sin x f ( II ) = 2 ( = ) sin ( =[ ) f (I ) = TT ( ) 8 Knot a derivative 3. Given that 3x - tan y =4, what is - in terms of y ? (A) 3sin y (B) 3cost y 3 - s Y = 0 (C) 3 cos y cot y (D) - 3 A+9p2 COS ly dy 3 y' - s cos y y' =0 y ' 1 3 - 8 oz y ) = 0 - 25. Find 4. Given f(x) = In [arccot(2x)] , find f'(x). (A) f' ( x ) = - - 2 ficx ) = = Farccot ( 2xx] (arccot(2x)) (B) f' (x) = - (1+4x )arccot(2x)) 2 - 8 (C) f' (x ) =- (1+4x )(arccot(2x)) (D) f' ( x ) =- (1+ 2x )(arccot(2x)) 5. Given h(x) = f(g(x)), use the graph to the right to find h'(4). - 6- inc (A) (B " ( 4 ) = f' ( g (x ) ) + g' ( x) (C (D 5 hi (w ) = f ' ( g ( 4) ) + g'( 4) = f' ( 5 ) + 6. If f (x) = In (#- x), then f'(x) = (A) x 2 x2 + 1 1+ x (B) 7 3 - 1 ficx ) = Z(#- x ) - In ( - 2 x-2 ) X 2 (C) x- + 1 1 - x (D) - 167. Find f' (x) for f (x) = (3x2+5)?. (A) f' ( x ) = 42x(3x2+5)6 BXS' (x) = 6(3x2+5)6 CD'( x) = 42x(3x2 + 567) (1) f' (x) = 6(6*) 6 f ( x ) = 21 * 2 + 5 + = 42x 8. Consider the function f(x) = x - x-11 . =derivative a. Find the instantaneous rate of change of f (x) when x = 3. f ( x ) = 32 - 3- 11 9 - 3 - 11 5 b. Write an equation of the line tangent to f at the point where x = 3. y- yl = m (x- xi) 2 x - 1 2 ( 3) - 1:5 4- 5 =-5 ( x-3) 4 -5 = -5x +15 ECF y =-5 x + 20 - 10 U9. Consider the following information in the chart. f(x) g(x) f' (x) g' (x) f"( x) g" (x) 1 -3 O 2 10 2 16 2 1 12 NIH 2 a. If h(x) = f(g(x)), find h'(1). h ' ( 1 ) = f ' ( y ( x ) @ y' ( x ) 2 1- 7 + 2 n' ( 1) = f' (g (is + gicI) "' (1) = f) ( - 5 ) + 2 b . If j (x ) ( x )(8 (f (x) ) , find j'(1 ). J ' ( 1 ) = x . " ( F ( x ) ) . f ' (x ) = (-161 5 product rule J ' ( 1 ) = 1 . g' ( 2 ) . . 4 c . Find ( f-1 ) ' ( 2 ) . : 1 . 4 . - 4 ( f - 1 ) ( 2 ) 1 1 - 14