Application of derivatives Questions and Answers

a Determine whether the Mean Value Theorem applies to the function f x 2 x2 on the interval 1 2 b If so find the point s that are guaranteed to exist by the Mean Value Theorem a Choose the correct answer below OA Yes because the function is continuous on the interval 1 2 and differentiable on the interval 1 2 OB No because the function is continuous on the interval 1 2 but is not differentiable on the interval 1 2 OC No because the function is not continuous on the interval 1 2 and is not differentiable on the interval 1 2 OD No because the function is differentiable on the interval 1 2 but is not continuous on the interval 1 2

3 Determine g x given that g x x x 1 2 3 4 g 16 1 and

x y 4x 3y 3 12 Submit Qu to solve the system O No solution O Infinite number of solutions Question Help Message instructor

Determine whether Rolle s theorem applies to the function shown below on the given interval If so find the point s that are guaranteed to exist by Rolle theorem f x x x 1 0 1 Select the correct choice below and if necessary fill in the answer box to complete your choice O A Rolle s Theorem applies and the point s guaranteed to exist is are x Type an exact answer using radicals as needed Use a comma to separate answers as needed OB Rolle s Theorem does not apply

Find the volume of the given solid under the surface z 4xy and above the triangle with vertices 1 1 4 1 and 1 2

Sketch a graph of f x 5 4 3 2 1 5 4 3 2 1 Clear All Draw 1 2 3 5 1 2 x 1 3 2 3 4 5

Find the horizontal intercepts of the function f x 3x 3 1 The intercepts are at x

Solve 7 8 Give your answer as an interval

Evaluate the following line integral along the curve C x y x y ds C is the line segment r t t 5t 8 for 0 st 3 x y ds

Which function graphed below is an EVEN function LIN TYTU Ho do F11 17 4

A function f x is an EVEN function If f 4 2 which other point lies on the graph of g x 4 2 4 2 4 2 2 4

A system of equations is given in which each equation is written in slope intercept form Determine the number of solutions If the system does not have one unique solution state whether the system is inconsistent or whether the equations are dependent y x 2 y The system has one solution The system has no solution The system is inconsistent The equations are dependent The system has infinitely many solutions The system is inconsistent The equations are dependent X EU

Find the future value for the annuity due with the given rate Payments of 15 000 for 10 years at 0 35 compounded monthly The future value of the annuity due is Do not round until the final answer Then round to the nearest dollar as needed

What is meant by a sinking fund List some reasons for establishing a sinking fund What is meant by a sinking fund Choose the correct answer below A an investment fund set up to receive periodic payments which increases in value over time B an investment fund into which only a single deposit is made which increases in value over time OC an investment fund with a negative interest rate which decreases in value over time OD an Investment fund that makes periodic payments to its investor which decreases in value over time List some reasons for establishing a sinking fund Select all that apply A to repay bonds that a corporation or municipality has issued B to provide for investment of a single lump sum of money such as an inheritance C to provide fixed income through periodic regular withdrawals from the fund D to retire a preferred stock that a company has issued E to provide for replacement of fixed assets F to provide an account into which varying amounts of money can be deposited at irregular intervals

The total cost of producing a type of boat is given by C x 17000 20x 0 02x where x is the number of boats produced How many boats should be produced to incur minimum cost Answer How to enter your answer opens in new window Keypad Keyboard Shortcuts

A rocket is launched upward with a velocity of 288 feet per second from the top of a 65 foot building What is the maximum height attained by the rocket

the minimum f x 4sinx 2 and maximum value of the fol 6 Maximum 2 Submit Answer

where t is days of practice For some tasks a sigmoid learning curve is used to model proficiency Suppose the percent proficiency is given by the model P t 100 1 30e 0 2 Find the inflection point the point where additional practice starts producing diminishing returns Give your answer accurate to at least 2 decimal places days

K Write a polynomial function that imitates the end behavior of the graph shown to the right The dashed portion of the graph indicates that you should focus only on imitating the left and right behavior of the graph and can be flexible about what occurs between the left and right ends Which of the following polynomial functions imitates the end behavior of the graph shown above Of x 6x 3x 4 Of x 9x 8x 3 Of x 10x 3x 3 Of x 8x 4x 10

A point on the terminal side of an angle 0 in standard position is 10 6 Find the exact value of each of the six trigonometric functions of 0

The domain of the function g is 0 8 The range of g is 6 1 2 What is the domain of g Use inf for as in inf inf means 0 00 Do not enter any spaces in the answer

Express 5 70x10 3 g in standard notation respecting significant figures 0 0057 g 0 00570 g 5700 g 570 g

A chemistry student measures width length and height of a rectangularly shaped object W 1 33 cm L 2 45 cm H 0 58 cm What is the correct way to express the volume of the object respecting rules for significant figures and proper unit 1 88993 cm 1 9 cm 1 89 cm 1 89 cm

Given y 300 4x 2 45 2 45 is the O x intercept Oslope none of the listed answers 2 45 is the x intercep y intercept

Solve 1 3 2 4 1 6 000 1 22 24 11 12 05 6

Solve the following equation for D A BC D OD A BC OD BC A OD BC A OD A 1 BC

A student need to solve for n in PV nRT What is the proper way to rearrange the above equation to solve for n n PVRT n PV RT On PT RV n RT PV

Given 5 0 x 7 0 25 x 10 0 12 9 5 O 7 2 O 14

A student need to solve for P in P T1 P2 T2 What is the proper way to to rearrange the equation above to solve for P OP1 P2T1 T2 OP1 P2T2T1 P T2T1 P2 P1 P T2 T1

Given the function f x 2 compute the left endpoint Riemann sum using n 5 on the interval 2 2 help numbers L5

Plot the point whose coordinates are 3 2 0 Select one a O b O C O d

a Find the Riemann sum for f x x 2 sin 2x 0 x 3 with six terms taking the sample points to be right endpoints Give your answer correct to six decimal points R6 b Repeat a with midpoints as the sample points M6

Find a Cartesian equation for the curve cos 20 25 Identify the curve O ellipse O circle O hyperbola Oline

Find the area of the shaded figure rounded to two decimals Assume x 3 and y 4 A x 60

Marketers for a drugstore chain chose two resort areas to test market a new sunscreen lotion After a summer of varying the selling price and recording the monthly demand the marketers arrived at the demand table shown to the right where y is the number of bottles of sunscreen purchased per month in thousands at x dollars per bottle XX y 5 0 5 5 6 0 6 5 7 0 2 0 1 8 1 6 1 3 1 1 A Use the method of least squares to find a demand equation The demand equation is y Type an expression using x as the variable Round to the nearest hundredth as needed

Use the gra tion to identify its domain and its range Select the correct choice below and fill in the answer box to complete your choice OA The domain can be best described using interval notation The domain is OB The domain can be best described using the roster method The domain is x x Use a comma to separate answers as needed O Show Transcribed Text 96 Ay 13

Note You can click on graphs to view them in a separate window pi 2 2 3 pi 2 P 3pi 2 Riemann sum for y 5 sina on 0 r The rectangles in the graph to the left illustrate a on the interval 0 The value of this Riemann sum is Riemann sum for f z 5sin

Find the average value of the function over the shaded region f x y 9x y 42 12 17 4 0 2 15 8 1 2 1 2 y 1x2 2 x

Find the least squares line for the points 4 3 6 6 8 0 and 9 9 Graph the data and the least squares line on the same axes

7 3 2 A graph of f x z is shown The numbers shown represent the geometric area of the regions above 0 1 Evaluate the following definite integrals a 160 de b 2 3 d c z 2 dx C d z 2 3 dx help numbers

11y 9 8 2311 10 9 8 7 6 5 4 3 2 1 Graph of y f x 5 6 7 8 9 10 11 A graph of f x 6 2x is shown Using the geometry of the graph evaluate the definite integrals 2 0 a 6 2x dx b f 6 6 2x dx c 6 C 6 2x dx d f 6 6 2x dx e 18 18 6x dx help numbers

the following exercises evaluate each integral in terms of an inverse trigonometric function 3 2 391 392 0 1 2 1 2 dx 1 x dx 1 x

Find the least squares line for the following data X 2 680 Y 1 1 0 1 2 y 0 3x 1 2 y 0 13x 1 2 y 0 13x 1 2 y 0 3x 1 2

the following exercises evaluate the definite integral 2 355 356 1 2x x 3x 3x x 4 tan x dx dx

The productivity of a major manufacturer of microwave ovens is given approximately 0 1 0 9 by the Cobb Douglas production function f x y 45x0 y with the utilization of x units of labor and y units of capital If the company is currently utilizing 4500 units of labor and 2000 units of capital find the marginal productivity of labor to the nearest unit 32 units 129 units 217 units 2 units

Use Lagrange multipliers to maximize f x y 5xy subject to x y 6 max f x y f 3 3 45 max f x y f 3 3 45 max f x y f 3 3 45 max f x y f 3 3 45

Suppose that the labor cost for a building is approximated by C x y 10x 2y 80x 420y 18 000 where x is the number of days of skilled labor and y is the number of days of semiskilled labor required Find the x and y that minimize cost C x 4 y 105 x 105 y 42 x 42 y 315 Ox 8 y 210

The surface area of a human body in square meters is approximated by A 0 202W 425 H 725 where W is the weight of the person in kilograms and H is the height in meters Find A if W 74 and H 1 61 FERD 02 03 m 1 83 m 1 87 m 1 78 m

Find the value for f 4 8 if f x y xy x 258 136 40 36

Solve for h 5 h 3 1 2 D Write your answer as a fraction or as a whole or mixed num h