2. (10 points) Find the absolute maximum and absolute minimum values of f on the given inter- val. (Show process! No process - No credit!) f (x) = In(x2 - 2x + 6), [-1, 2] Value! Abs. Max Value is: ( 216, 2. 197 ) Abs. Min Value is: (161.609 f ( n ) = In ( 2 - 2x+6) In ((1) 3- 2(1) + 6 ) fi(x ) 2x - 2 O min ( 1 , 1.604 ) ( 1 , 2. 197 ) 2 - 2 = 0 ( 2, 1.791) an = 2 - 2 n = 1 1 min at 1Math 2211, Calculus I Test 3B, Page 3 of 5 6. (8 points) The graph of the dernative f in [0, 6] is shown. (No need to show process.) f ( x ) a) On what intervals is f increasing? ( - 0 , 2 ) 1) ( 4 / 5 .5 ) b) On what intervals is f decreasing? ( 2, 4 ) 1 ( 5 5 , 6) c) At what values of x does f have a local maximum? -1 , 5 d) At what values of x does f have a local minimum? 3 V 7. (8 points) The graph of the derivative f' in [0, 6] is shown. (No need to show process.) P ( x ) a) On what intervals is f increasing? ( 0 , 1 ) V ( 1 3 0 ) U ( 4 , 5 ) b) On what intervals is f decreasing? ( 1 , 2 ) ( 2 8 ) ( 5 , 6) c) At what values of x does f have a local maximum? 1 x 5 d) At what values of x does f have a local minimum?Math 2211, Calculus I Test 3B, Page 2 of 5 3. (8 points) Determine whether the given function satisfies the three hypotheses of the Rolle's Theorem on the given interval. If so, find all numbers c that satisfy the conclusion of Rolle's Theorem. (Show process! No process - No credit!) 2 2 + 1 f ( 2 ) = x+ 2 ' f ( x) is continuous on [- 3, 3] [-3, 3] f '(n ) existson (- 3, 3) No 2x ( 2+ 2 ) - (2 +1) 1 = 0 ( vit 2 ) 2 an2+ 4 x- 20-1=0 2n2+ 421-1=0 f ( - 3 ) = 2 0 - 3 ) + 1 = 5 f ( 3 ) = 2 ( 3 ) + 1 = 1.4 4+ doesn't - 3 + 2 3 + 1 satisfy the. 4. (8 points) Determine whether the given function satisfies the two hypotheses of the Mean Value third condition Theorem on the given interval. If so, find all numbers c that satisfy the conclusion of Mean Value Theorem. (Show process! No process - No credit!) f (x ) = x2 - 3x+6, [0, 2] f (x ) is continuous on [o, 2] F/(x) exists on ( 0, 2 ) 4 - 6 2 - 0 - 1 included in [0, 2]