f on the same coordinate axes.

Transcription

1 Calculus AB 0 Unit : Station Review # TARGETS T, T, T, T8, T9 T: A particle P moves along on a number line. The following graph shows the position of P as a function of t time S( cm) (0,0) (9, ) (, ) t When is the particle moving left? When is the particle not moving? (, ) (6, ) (, ) On what interval is the speed the greatest? Graph the particle s velocity graph: Graph the particle s speed graph: T) Determine whether each labeled point is an absolute maimum or minimum, a relative maimum or minimum or none. B F A: B: C: C D D: E: F: A E T/T8) Given the graph of f, graph f ' f and " f on the same coordinate aes. 5 y 5 5 f 5

2 Calculus AB 0 Unit : Station Review # TARGETS T0, T, T, T5, T6, T9 Given the graph of f ( ), Given the graph of f '( ), f ( ) f '( ) y y Identify the following of f ( ) : (estimate values) Identify the following of f ( ) : (estimate values) Increasing: Decreasing: Relative Min: Relative Ma: Concave up: Concave down: Point(s) of Inflection: Increasing: Decreasing: Relative Min: Relative Ma: Concave up: Concave down: Point(s) of Inflection: T9) Sketch a function f() that has the following characteristics. A) f (0) = f () = 0 f ( 5) =, f (0) = 0, B) f () = 6, f (8) = 0 f '( ) > 0, if < f '() = 0 f '( 5) = undefined f '() = 0, f '( ) > 0 when < 5 f '( ) < 0, if > f '( ) > 0 when 5 < < f ''( ) < 0 f '( ) < 0 when > f ''( ) < 0 when < < 5 f ''( ) > 0 when 5 < < 0 f ''( ) < 0 when 0 < <

3 Calculus AB 0 Unit : Station Review # TARGETS T5, T6 & T7 0( + ). Given f ''( ) =, find the intervals of concavity and the -coordinates of the point(s) of inflection, ( ) if they eist. Use valid calculus and appropriate labels. Possible Pts of inflection (-coord): Concave Up: Concave Down: Pts of inflection (-coord):. Find all relative etrema (if they eist) using the Second derivative test. Show and organize your work using valid calculus. Use the appropriate labels. f ( ) = sin + cos, [0, π ] Rel Min Rel Ma

4 Calculus AB 0 Unit : Station Review # TARGET T, T, T6, T0, T. Find all critical values, relative ma/mins ( -coordinates only) and interval(s) of increasing and decreasing given f '( ) = using the st derivative test. Use valid calculus and appropriate labels. Crit Values: Rel Ma: Rel Min: Inc: Dec:. Find all absolute ma/mins on the closed interval given f ( ) = cosπ [ 0, ] Use valid calculus and 6 appropriate labels. Absolute Ma: Absolute Min:. A company uses the formula C( ) = , 0 00 to model the unit cost in dollars for producing coffee mugs. Find the number of coffee mugs that yields a minimum cost to the company.

5 Calculus AB 0 Unit : Station Review #5 TARGETS UT, UT. A circular conical reservoir, verte down, has depth 0 ft and radius of the top 0 ft. Water is leaking out so that the surface is falling at the rate of ½ ft per hour. The rate, in cubic feet per hour, at which the water is leaving the reservoir when the water is 8 feet deep is?. A balloon is being filled with helium at the rate of the surface area is increasing when the volume is 08 ft /min. The rate, in square feet per minute, at which π ft is?. A hot air balloon rising straight up from a level field is tracked by a range finder. The range finder is on the π ground 500 feet away from the balloon s lift off point. At the moment the range finder s elevation angle is, the angle is increasing at the rate of 0. radians per minute. How fast is the balloon rising at that moment?

6 Calculus AB 0 Unit : Station Review #6 TARGETS T5, T7, T8, T9 + T8) Determine whether the Mean Value Theorem can be applied to the function f ( ) =, on the closed interval [ ½, ]. You must show all the justification as to why or why not the MVT can be applied. If the Mean Value Theorem can be applied, find all values of c (show work) in the open interval (½, ) that work. T7) Determine whether Rolle s Theorem can be applied to the function f ( ) =, on the closed interval [ -, ]. You must show all the justification as to why or why not Rolle s Theorem can be applied. If it can be applied, find all values of c (show work) in the open interval ( -, ) that work. T5) Eplain what the Etreme Value Theorem guarantees and state the requirements necessary to apply the theorem. Guarantees: Requirements: T9) A runner runs a 00 yard dash in 0 seconds. Assume that the function s(t) which gives his position relative to the starting line is continuous and differentiable. Show the runner must have been running at 5 yards per second at some point during his run, and state what theorem guarantees this.