MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 MAC Summer C 6 Worksheet (.,.,.) Table Names MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sketch the graph of the function and determine whether it has an absolute etreme values on its domain. ) = -, < ) - - A) absolute maimum at = ; no absolute minimum B) absolute maimum at = ; absolute minimum at = C)absolute maimum at = ; no absolute minimum D) absolute maimum at = ; absolute minimum at =

2 Find the etreme values of the function and where the occur. ) = - + A) Local maimum at (, ). B) Local maimum at (, ), local minimum at (, -). C) None D) Local minimum at (, -). ) ) = e - + e - A) Minimum value is e ( - ) at = - ; maimum value is e - ( + ) at =. B) Maimum value is e - ( + ) at = ; no minimum value. C)Minimum value is e ( - ) at = - ; no maimum value. D) None ) + ) = + + A) None B) The maimum is at = ; the minimum is at = -. ) C)The maimum is at = ; the minimum is - at = -. D) The maimum is - at = ; the minimum is at = -. Find all possible functions with the given derivative. ) = - 6 A) C B) C C) C D) C ) 6) r = + θ 6) A) r = θ - θ B) r = θ - θ C)r = θ + θ D) r = θ + θ

3 Find the etrema of the function on the given interval, and sa where the occur. 7) sin + cos, π A) local maima: at = π and at = π ; 7) local minima: at = and - at = π B) local maima: at = π and at = π ; local minima: at = and - at = 7π C)local maima: at = and - at = π ; local minima: at = π and at = π D) local maima: at = and - at = 7π ; local minima: at = π and at = π Find the absolute etreme values of the function on the interval. 8) F() = -., 8) A) absolute maimum is at = ; absolute minimum is - at = B) absolute maimum is - at = ; absolute minimum is - at = - C)absolute maimum is - at = ; absolute minimum is - at = - D) absolute maimum is - at = ; absolute minimum is - at = Use the maimum/minimum finder on a graphing calculator to determine the approimate location of all local etrema. Hint "nd + Trace" buttons. 9) f() = A) Approimate local maimum at -.; approimate local minimum at. B) Approimate local maimum at -.; approimate local minimum at. C) Approimate local minimum at -.; approimate local maimum at. D) Approimate local minimum at -.; approimate local maimum at. 9) ) f() = A) Approimate local maima at -. and -.9; approimate local minima at -.7 and.9 B) Approimate local maima at -. and -.6; approimate local minima at -.8 and.899 C) Approimate local maima at -. and -.7; approimate local minima at -.7 and.9 D) Approimate local maima at -. and -.6; approimate local minima at -. and.88 )

4 f(b) - f(a) Find the value or values of c that satisf the equation = f (c) in the conclusion of the Mean Value Theorem for b - a the function and interval. ) f() = ln ( - ), [, 6] Round to the nearest thousandth. A).8 B).88 C) ±.8 D).8 ) ) f() = + +, [-, -] ) A) -, B) -, - C) - D), - Using the derivative of f() given below, determine the intervals on which f() is increasing or decreasing. ) f () = ( - )(8 - ) A) Decreasing on (-, -) (-8, ); increasing on (-, -8) B) Decreasing on (-, ); increasing on (8, ) C)Decreasing on (-, ) (8, ); increasing on (, 8) D) Decreasing on (, 8); increasing on (-, ) (8, ) ) ) f () = ( + ) e - A) Never increasing; decreasing on (-, -) (-, ) B) Never decreasing; increasing on (-, -) (-, ) C)Never decreasing; increasing on (-, ) (, ) D) Decreasing on (-, -); increasing on (-, ) )

5 Solve the problem. ) Find the table that matches the given graph. ) a b c A) C) f () a b c - f () a does not eist b does not eist c - B) D) f () a does not eist b c - f () a does not eist b c

6 6) Find the graph that matches the given table. 6) f () -. A) B) C) D) Find the absolute etreme values of the function on the interval. 7) f() = - e -, - < < A) No minimum value and no maimum value B) Minimum value is - at = ; no maimum value C)Maimum value is - at = ; minimum value 7) D) Minimum value is - at = ; maimum value is - e at = Using the derivative of f() given below, determine the critical points of f(). 8) f () = (- ) ( + 8) A) -,, 8 B) -,-8, C) -8, D) -, 8 8) Identif the function's local and absolute etreme values, if an, saing where the occur. - 9) h() = + + A) local minimum at = -; no local maima B) local minimum at = -; local maimum at = C) no local etrema D) local minimum at = -; local maimum at = 9) 6

7 ) f() = A) local maimum at = -; local minimum at = B) local maimum at = -; local minimum at = C)local maimum at = ; local minimum at = - D) local maimum at = ; local minimum at = - ) Find the derivative at each critical point and determine the local etreme values. ) = / ( - ); A) Critical Pt. derivative Etremum Value = =. Undefined local ma minimum -.7 B) Critical Pt. derivative Etremum Value = =. maimum minimum -.7 ) C) Critical Pt. derivative Etremum Value = Undefined local ma =. minimum -.7 D) Critical Pt. derivative Etremum Value = Undefined local ma =. minimum.787 -, < ) = + -, A) Critical Pt. derivative Etremum Value = undefined local min B) Critical Pt. derivative Etremum Value = undefined local min ) = local ma 9 = local ma 7 C) Critical Pt. derivative Etremum Value = - undefined local min D) Critical Pt. derivative Etremum Value = undefined local min = local ma 7 = local ma 9 7

8 Find the open intervals on which the function is increasing and decreasing. Identif the function's local and absolute etreme values, if an, saing where the occur. ) ) A) increasing on (-, ) and (, ); decreasing on (, ); absolute maimum at (, 7) and(,); absolute minimum at (-, ) and (, ) B) increasing on (-, ) and (, ); decreasing on (, ); absolute maimum at (, 7); absolute minimum at (-, ) and (, ) C)increasing on (, ); decreasing on (, ); absolute maimum at (, 7); local maimum at (, ); absolute minimum at (-, ) and (, ) D) increasing on (-, ) and (, ); decreasing on (, ); absolute maimum at (, 7); local maimum at (, ); absolute minimum at (-, ) and (, ) Plot the zeros of the given polnomial on the number line together with the zeros of the first derivative. ) = ( - )( + ) ) A) B) C) D)

9 Find the location of the indicated absolute etremum for the function. ) Minimum h() ) A) = B) = - C) = D) = - Find the largest open interval where the function is changing as requested. 6) Decreasing f() = - A) -, B) -, - C) -, D), 6) 7) Increasing f() = + A) (-, ) B) (, ) C)(, ) D) (-, ) 7) Determine all critical points for the function. 8) f() = A) = and = 6 B) = and = C) = - and = D) = 8) Determine whether the function satisfies the hpotheses of the Mean Value Theorem for the given interval. 9) s(t) = t( - t), -, A) Yes B) No 9) 9

10 Determine from the graph whether the function has an absolute etreme values on the interval [a, b]. ) ) A) No absolute etrema. B) Absolute minimum onl. C) Absolute maimum onl. D) Absolute minimum and absolute maimum. Find the function with the given derivative whose graph passes through the point P. ) f () = -, P(, ) A) f() = - B) f() = C)f() = - + D) f() = )