Application of derivatives Questions and Answers

2 Find the period of y cot 2

4 Let f 0 tan and g 0 cot 0 Which of the following statements is true A If f 0 0 g 0 0 B If f 0 0 g 0 0 C f 0 g 0 when 0 F D f 0 g 0 0 for all 0

7 Graph y cot x 3TT 2 TT y 34 N TT 2 0 2 TT 2 TT 3TT 2 X

Write the equation of a tangent function with a period of 3r and a vertical shift up 4 units

a I only f x 5 c lim x 2 X 2 d lim f x 7 1 g is continuous at x c II lim g x exists x c III lim X C 7 g x g c x c a lim f x 5 b m f x lim f x 2 x 2 dy 7 20 x 2 exists b Ill only must be true 3 If f is a differentiable function such that f 2 5 and f 2 7 which of the following statements could be false c I and II only Q 11 II and III 2 7 Product Rule 1 Let f be a differentiable function with f 2 7 and f 2 2 Let g be the function defined by g x x f x Which of the following is an equation of the line tangent to the graph of g at x 2 a y 7 2 x 2 b 28 2 20 x 2 c y 7 x 2

16 If g is a differentiable function such that g x 0 for all real numbers x and if f x x 4 g x which of the following is true A f has relative maxima at x 2 and x 2 B f has relative minima at x 2 and x 2 C f has a relative minimum at x 2 and a relative maximum at x 2 D has a relative maximum at x 2 and a relative minimum at x 2

1 In the right angle triangle 4ABC where ZC is 90 ZA 42 and side c 45 cm determine the unknown side a Round your answer to the nearest centimetre a sin42 45 A 30 cm B 32 cm C 29 cm D 31 cm 2 Use right angle trigonometry to determine ZA Round your answer to the nearest degree b 12 C A 36 B 45 C 30 D 37 c 15 B unknown ride a Bound your answer to the nearest tenth of a unit

Find the instantaneous rate of change of the function at the given f x f a x a x value using the form lim x a 2 y 3x2 4x 7 at x

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

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

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

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

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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

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

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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

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

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

In at x 0 2

x tan cos x at x 1

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

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

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

Perform the operation s and write the result in standard form Simplify your answer completely 4 3 5i

y x x 16 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 40 20 MA 2 2 6 20 40 6 6 4 4 y 40 20 20 40 2 4 X X 6 6 4 4 2 40 y 20 20 40 y 40 20 20 40 2 2

Write an equation for the parabola in standard form Use a graphing utility to graph the equation and verify your result f x 10 5 3 2 10 5 0 7 5 10 X

Write the quadratic function in standard form f x x 18x 76 f x Sketch its graph 15 10 5 15 10 5 axis of symmetry x intercept x f x f x x f x 15 10 5 5 10 15 f x 15 10 5 5 10 5 15 5 10 10 15 15 X X 15 10 5 smaller x value 15 10 5 f x 15 10 5 5 10 15 O Identify the vertex axis of symmetry and x intercept s If an answer does not exist enter DNE vertex f x 15 10 5 5 10 15 5 5 10 10 15 15