Application of derivatives Questions and Answers

Find the absolute maximum and absolute minimum values of f on the given interva f t 2 cos t sin 2t absolute minimum value absolute maximum value 0 EN

DETAILS 3 0 11 Points Use the graph to state the absolute and local maximum and minimum values of the function Assume each point lies on the gridlines Enter your answers as a comma separated list If an answer does not exist enter DNE y 5 ww y f x 24 1 absolute maximum value absolute minimum value local maximum value s local minimum value s SCALCET9 4 1 005 2 3 4 5 6 X

Question 18 4 3 2 middle 2 highest 2 7 1 3 v 18x For the above rational function f x 4x 2 5 identify its three inflection points algebrically using its derivatives Leave answers in 4 decimal places when appropriate lowest

Find the absolute maximum and absolute minimum values of f on the given interval f x 6x 18x 54x 5 2 4 absolute minimum value absolute maximum value

Find the numerical value of each expression Round your answers to five decimal places a sinh 2 b sinh In 2

For each of the numbers a b c d r and s state whether the function whose graph is shown has an absolute maximum or minimum a local maximum or minimum or neither a maximum nor a minimum Enter your answers as a comind ab cdr IMM E absolute maximum absolute minimum local maximum local minimum neither a maximum nor a minimum

If cosh x sinh x tanh x coth x sech x csch x and x 0 find the values of the other hyperbolic functions at

Find the derivative g x g x sinh2 x

nd the derivative x f x ex cosh x

Prove the identity Recall sinh a b sinh a cosh b cosh a sinh sinh 2x 2 sinh x cosh x sinh 2x sinh x sinh x 2 sinh x cosh x cosh x sinh x

5 2 The new cookbook you just got gives all the oven temperatures in degrees Celsius but your oven uses degrees Fahrenheit Additionally your oven runs hot and you always have to decrease the prescribed temperature by 15 F Write an expression using a composition of functions that will determine how high you have to preheat your oven when a recipe from your new cookbook calls for a temperature of t C Hint C F 32 and C 32 are the equations to convert between degrees Celsius C and degrees Fahrenheit F 9 9 F C

9 The graph of a function f is shown on the interval 7 5 Let g x 5x 8 a Find f g 1 b Find g f 3 O M 3 2 1 4 8 7 6 5 4 3 2 1 0 1 2 3 5 61 1 2 3 4 5 6

8 Let f x x 2 and g x A f g 3 B g f 11 C g 2 D f g 5 4 2x 6 Which of the following is defined

6 Given the functions f x x and g x x 2 which of the following graphs could represent y g f x A 64 5 O 2 8 9 10 11 E B D 3 10 0 10 11 10 TI

5 If h f x 3 x 7 find a possible expression for h x and f x

3 A table of selected values is given for the functions f and g The domain of both functions is all real numbers f x x g x 5 11 11 3 8 0 6 4 3 8 6 XC 3 3 5 2 5 1 0 2 4 7 Find f g 4

Find the following limits 5 3 4 x 3x 2 a lim xx 5 4 x x 3x 2 b lim

Evaluate the limit using L Hospital s rule if necessary sin 8x lim 0 sin 7x cos x cos x Question Help Video X syntax incomplete an retr

Let f x H 3e 2 1 e The graph of f is given below Use the graph of f to determine the given limits Enter DNE if a limit fails to exist except in case of an infinite limit If an infinite limit exists enter or as appropriate 5 4 1 5 4 3 2 1 lim f x I lim f x SO 2 2 2 3 4 5 I 2 3 4 5

Use the Intermediate Value Theorem to show that the following function has a zero in the given interval Approximate the zero correct to two decimal plac f x 3x 9x 9x 9 4 3 Select the correct choice below and if necessary fill in the answer box to complete your choice 0 and f 3 0 OA The polynomial has a real zero on the given interval because f 4 Type integers or decimals OB The polynomial has a real zero on the given interval because f 4 0 and f 3 Type integers or decimals 0 OC The polynomial has a real zero on the given interval because f 4 and f 3 are both positive OD The polynomial has a real zero on the given interval because f 4 and f 3 are both negative

2 Suppose f x 3x x 2 x 7 Determine where the tangent line to y f x is horizonte

201 Find f x if f x H T 32

Use the rational zeros theorem to list the potential rational zeros of the polynomial function Do not attempt to find the zeros 11 8 f x 2x 1 x 2x 52 Find the potential rational zeros Choose the correct answer below OA 1 1 2 2 4 4 13 13 26 26 52 52 OB 1 1 2 2 4 4 13 13 52 52 OC 1 1 2 2 4 4 13 13 52 52 1 1 2 2 OD 1 1 2 2 4 4 13 13 26 26 52 52 1 1 2 2 1 22 1 52 52 1 1 13 13 2 2 22 1 1 52 52 31 1 1 32 52 52 1 1 13 13 2 2 22

3 f x x 12x 34x 16 to facto11 The real zero s of f is are 8 2 2 2 2 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Use a comma to separate answ Factor f f x Factor completely Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

zeros theorem to list the potential rational zeros of the polynomial function Do noteltempt to find the z f x x5 8x 8x 9x 5 Find the potential rational zeros Choose the correct answer below OA 5 5 11 5 5 1 1 OB 1 1 5 5 11 OC 1 1 5 5 5 5 OD 1 1 5 5

10x 13x 22 f x x 10 The real zero s of f is are Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed

the remainder theorem to find the remainder when f x is divided by x 2 Then use the factor theorem to determine whether x 2 is a factor of f x f x 3x 2x 10x 10 The remainder is 6 Is x 2 a factor of f x 3x 2x 10x 10 Yes No 09 1 of Points 0 of 1

Use the remainder theorem to find the remainder when f x is divided by x 2 Then use the factor theorem to determine whether x 2 is a factor of f x f x 3x 2x 10x 10 The remainder is

Given the function defined by f x x x 4x 4 Find the zeros off Write an equation of the line tangent to the graph of fat x 1 a b

Complete the sentence below If f is a polynomial function and x 5 is a factor of f then f 5 If f is a polynomial function and x 5 is a factor of f then f 5

3 4 Find the equation of the tangent line to the curve f x x 2x 6 at the point 2 6 4 marks

Show all your work Clearly indicate the methods used as you will be graded on the correctness of your method as well as your accuracy of your final answer Each question is worth 10 points Please keep your work as neat as possible so I may easily grade and return the problem set quickly 1 The line x c where c 0 intersects the cubic y 2x 3x 9 at a point P and the parabola y 4x 4x 5 at point Q a If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point O find the value of c where c 0

Write the expression in the standard form a bi 7 5 6i 7 5 6i Simplify your answer

Write the expression in the standard form a bi 9 4i 2 i 9 4i 2 i Simplify your answer

A GPCRs activate G proteins by reducing the strength of GDP binding allowing GDP to dissociate and GTP which is present in much higher concentrations to bind What would happen if the affinity of Ga for GDP were reduced but the affinity for GTP remained unaffected Explain your reasoning make sure to explain the effect on amount of pathway signaling as compared to non mutated Ga and then why

To find the derivative of y 3x 6x 4 would require the chain rule What functions f x and g use to find y if y f g x

Which of the following is an equivalent expression to f g x g f x x g x f x g x f g x

Does the sequence a converge or diverge Find the limit if the sequence is convergent a 2 1 Select the correct choice below and fill in any answer boxes within your choice OA The sequence converges to lim n c Simplify your answer OB The sequence diverges an 0 of 12

The domain of f is 0 00 Type your answer in interval notation b Choose the correct graph of f Ay A The horizontal asymptote of f is y 5 Simplify your answer OB There is no horizontal asymptote the inverse of f Ay d Find f f x Simplify your answer G C c From the graph determine the range and any asymptotes of f The range of f is 5 00 Type your answer in interval notation Determine the horizontal asymptote of f if it exists Select the correct choice and if necessary fill in the answer box to complete your choice C Q OD Clear all

implify 2x 3x 5

Use integration by substitution and the Fundamental Theorem to calculate the definite integral NOTE Enter the exact answer S X o 1 x 2 dx 4 5

2 Find the equations of the tangent lines to the curve y x x 2 that pass through he point 3 2 Include a sketch to illustrate your solution 7 marks

B Find the range of a values for which the profit is positive Find the percentage rate of change of f x 102 28x at x 5 rounded to the nearest

Find the area of the region inside r 10 sin 0 but outside r 2 Graph the curves on a calculator Turn in a sketch of the curve

Find the area inside one leaf of the rose r 1 sin 5

Find the sum of the and y intercepts of any tangent line to the curve x y 10

If log x 15y x y 3 and y 4 1 find y 4 by implicit differentiation 4 1 An equation of the tangent line to the curve at the point 4 1 is

Find the sum of the x and y intercepts of any tangent line to the curve x y 10 FEB

dr Let A be the area of a circle with radius r If dt dA dt 2 find when r 2

Compute the following derivative d dx cot cot