High School Calculus Questions

of a race round all answers to the nearest tenth 10x 10 F t c Write a function representing the inverse of f x and interpret its meaning of x and y in context to the problem All work must be completed by hand and justified mathematically 6 points A Paragraph BI UV V Times New 12pt 7 15 All work must completed by hand and justified mathematically Type your work in using the time in seconds after the start V Fa 30 C

2 A math tutor makes 15 00 per hour in the tutoring lab at her school She earns an additional 7 50 more per hour overtime for any hours worked which exceed her normal 40 hr work week a Which graph depicts her toal salary for the week as a function of number of hours worked 4 points 1200 posi

1 Determine a b c and d so that the graph of y ax bx cx d has a point of inflection at the origin and a relative maximum at the point 2 4 Sketch the graph

4 Find an equation of the line through the first quadrant that cuts off the least area from the first quadrant

Consider f x cos x 2 cosx over one complete period beginning with x 0 a Find all values of x in this period at which f x 0 b Find all values of x in this period at which the function has a minimum Justify your answer c Over what intervals in this period is the curve concave up

3 Determine the following about the graph of the equation 8 6 a b y 3 X X Is the graph symmetric with respect to 1 The X axis 2 The Y axis 3 The origin Identify all asymptotes of the graph

2 Consider f x cos x 2 cosx over one complete period beginning with x 0 a Find all values of x in this period at which x 0

Standard 6 NR 4 1 The ratio of squirrels to pigeons in the park is 15 to 125 Which statement describes this relationship O There are 3 squirrels for every 25 pigeons in the park O There are 3 squirrels for every 5 pigeons in the park O There are 5 squirrels for every 3 pigeons in the park There are 25 squirrels for every 3 pigeons in the park

Suppose the following functions are graphed in the xy coordinate plane Which graph has x intercepts A y sin x 3 B y csc x 3 C y 3 sec x D Y CSC x

1 a What is the period of the graph of the function 5 Consider the function y sec b How far apart are the asymptotes on the graph of the function

4 Consider the graphs of f x sin 2x and g x csc 2x a Describe the transformations of the graphs of y sinx and y cscx that produce the graphs of f and g b List the four x intercepts of the graph of f c List four vertical asymptotes of the graph of g

2 Write an equation of a cosecant curve with asymptotes at x

Postmodernism is reminiscent of this earlier movement in its attempt to elude a specific definition Cubism Abstract Expressionism Pop Art

7 f x 3x 6x 1x 1 ax 3 x 1

6 f x Sax4 x 4 x 2 bx 5 x 2

What values of a and b would make the function differentiable at the given value of x 6 f x ax x 4 x 2 bx 5 x 2 r 1

3 Determine if the functions are differentiable at the given x value prove continuity first and then prove differentiability If needed f x co 2x x 10 x 5 50 14x x 5 5x 2x 1 x 3

Use the table to find the value of the derivatives of each function IL X 7 h x 5f x g x f x 5 f x 3 g x 2 g x 3

f x x 3x 22 4x 10 3x 22 x 3 x 3

1 f x 12e5x 7 cos x

No Calculator No Calculator No Calculator No Calculator No Calculator 5 10 5 800 A g only C f g and h 10 The graphs of the derivatives of the functions f g and h are shown above Which of the functions f g or h have a relative maximum on the open interval a x b yux B fonly D and g only

No Calculator No Calculator No Calculator No Calculator No Calculator 13 The absolute maximum value of f x x 3x 12 on the closed interval 2 4 occurs at x A 0 0 4 B D 2

14

8 Given f x 6 11 find all c in the interval 2 5 such that f c f 5 2 5 2 A 15 C 15 B 10 D 10

11 Let f be a function defined and continuous on the closed interval a b Iff has a relative maximum at c and a c b which of the following must be true I f c must exist II If f c exists then f c 0 III If c exists then c 0 A II and III only C III only B I and III only D II only SE

Part II Free Response Graphing Calculator Permitted Be sure to show all your work Point values are given in 6 h graph of f x 5 Let be a differentiable function defined on the interval 6 x 6 The figure above shows the graph of the derivative off which consists of 3 line segments and a semi circle on the interval 6 x 6 a State the critical values of f x on 6 x 6 and classify each as the location of a relative minimum relative maximum or neither of the graph of f x Justify your answer 3 points b On what interval s contained on 6 x 6 is f x increasing Justify your answer 2 points c For what value s of x contained on 6 x 6 does f x have a point of inflection Justify your answer 2 points d On what open interval s contained on 6 x 6 is f x simultaneously concave up and decreasing Justify your answer 2 points

3 The first derivative of the function fis given by f x esr 1 How many critical values does hav 5 on the open interval 0 10 Hint Sketch over the Window xmin 10 xmax 10 min 2 max 2 A Four B One C Seven D Five

40 36 5 cm W 28 cm 21 4 cm Find the length of side 18 0 cm

2 Graph y sin 2x TT V TT 2 1 5 1 0 5 0 0 5 TT 2 TT 3TT 2 2TT

3 Graph y sin x 1 T TT 2 3 2 1 0 1 TT 2 TT 3TT 2 2TT x

5 Consider the graph of y f x where f x 2 5 cos x a Identify the midline of the graph of f b Identify the period of f c Identify the range of f d Identify the amplitude of f

7T The period of the graph of y 7 sin Br 3 is 2 Find the value of B

Find the instantaneous rate of change of th function at the given x value Use the form f a h f a lim h 0 h 2 f x 4x 1 at x 2

Find the AROC of the function on the Given interval g x x 2 1 3

4 g x 5 at x 4 X

In at x 0 2

16 Use the table to the right to find the equation of the tangent line of the function r x 0 5f x 3g x at x 2 X f x f x g x 2 12 2 4 4 10 1 15

x tan cos x at x 1

3 Describe what is meant by the statement the period of y 1 sin x is 27

4 Graph y cos x for T x 4 3A y 0 1 TT 2TT 3TT 4TT X

6 For which of the following functions is it true that f x f x A f x B f x cos x C Both f x sina and f x cos x D Neither f x sinx nor f x sin x

1 When graphing y cos x on the xy coordinate plane describe what is measured on the x axis and y axis

Kai says the amplitude of y cos x is 2 since the distance between the maximum and the minimum value is 2 Is Kai correct Explain

y x5 5x 4x a Find the zeros algebraically Enter your answers as a comma separated list If there are no real zeros enter DNE X b Use a graphing utility to graph the function y O 4 4 4 2 y A 2 4 X 4 y M 4 2

19 1 point Jimmie invested 27 500 at 6 27 compounded continuously What will Jimmie s account balance be in 50 years 29 279 45 632 187 49 688 423 41 37 625 65

Find any asymptotes and holes in the graph of the rational function Verify your answers by using a graphing utility Enter your answers as a comma separated list If an answer does not exist enter DNE f x x 2x 1 7x x 8 vertical asymptote s hole s horizontal asymptote s X y X

Consider the following function f x 3x 8x 4 2x 3x 2 Find all vertical asymptotes horizontal asymptotes slant asymptotes and holes in the graph of the function Then use a graphing utility to verify your result Enter your answers as comma separated lists If an answer does not exist enter DNE vertical asymptote horizontal asymptote slant asymptote hole x y y x y

Write the quotient in standard form Simplify your answer completely 11 2 i

Perform the subtraction and write the result in standard form Simplify your answer completely 123i 4 7i

Perform the operation s and write the result in standard form Simplify your answer completely 4 3i 4 3i