Differentiation Questions and Answers

Solve log 5 x 4 log 9 4x Round your answer to the nearest tenth Do not include x in your answer If necessary include a leading 0 before the decimal point For example 0 5 instead of 5

ind f x 1 x x 3 4 2 f x 8 x 3 x 3x 3 2

Use the graph of f x to discuss the graph of y f x Organize your conclusions in a table and sketch a possible graph of y f x U D me function is never decreasing Af x 10 10 Q G Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f is increasing on the subinterval s Type your answer using interval notation Use a comma to separate answers as needed B The function f is never increasing

find the derivative of the given function y x e 3x y Ctype an exact unsuer

Solve 6 3 8 Enter an exact answer or round your answer to the nearest tenth Do not include x in your answer

Write log 3x in expanded form

find the derivative of the function 9 5x 8 7x 1 The derivative is y S CA 29 StXV is y los Jesen hibao wolker

2 Use algebra and the properties of to find the given limit If the limit does not exist Say so lim x 7x 18 2 X39

3 Find the derivative of the given function F x 6x52x x 4x 5 4

find the derivative of the function end 2 y 9 4x 75 6 crype an expression using x as the variable 24x2 dy

dr Let A be the area of a circle with radius r If dt 2 find dA dt when r 4

Question Enter the single logarithmic expression that is equivalent to 3 In 9 2 In 6 In 3 1 Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard below

Find a function of the form y A sin kx C or y A cos kx C whose graph matches this one n 10 9 17 15 12 Leave your answer in exact form if necessary type pi for 10

ind the derivative of the function 5x 8 y 6x 1 ne derivative is y

Find the integral xdx 7x 73 Option A 7x 3 B C 7x 3 C 2 G 4 7x 3 c 9 7x 356 C

Calculate the iterated integral 2 6x y 2x dy dx

The fur h x 3 Find h x for each x value in the table h x 0 X 1 0 h is defined by the following rule 1 0 0

Find the power series for the 2 function f x centered at 1 x 8 x 0 x

Find the exact value of the following expression tan JE 6 4

Consider f u mavg on 1 4 Vu Determine the interval over which f is continuous and the interval over which f is differentiable f is continuous on f is differentiable on Use the above information to determine if the Mean Value Theorem may be applied to f over 1 4 Select all that apply Yes the Mean Value Theorem may be applied to f on 1 4 No the Mean Value Theorem may not be applied to f on 1 4 since f is not continuous on 1 4 No the Mean Value Theorem may not be applied to f on 1 4 since f is not differentiable on 1 4 Determine the average rate of change of f over 1 4 etermine the value s of c guaranteed by the Mean Value Theorem

Find the exact value of the expressions cos a B sin a B and tan a B under the following conditions sin a 24 25 a lies in quadrant I and sin B 13 Blies in quadrant II

To evaluate S 5f x dx use the following property of the definite integral Then S kf x dx 6 1 5 5f x dx S f a f x dx f x dx

Find an angle with 0 0 360 that has the same Sine as 230 0 degrees Cosine as 230 0 degrees

Cost analysis A company with two different plants manufactures guitars and banjos Its production costs for each instrument are given in the following matrices Plant X Plant Y Materials Labor A B Find A B the average cost of production for the two plants SA FA Guitar intogors or decimals Banjo 49 32 103 120 A Guitar 68 59 93 125 Banjo B

f x Use the graphs of f and g and their tangent lines at 2 0 to find lim x 2 g x 2 125 y 2 1 1 2 X y 1 9 x 2 4 1 y 5 x 2 3 g 4 X

1 point Suppose y 5 cos 7t 27 6 In your answers enter pi for a What is the phase shift help numbers b What is the horizontal shift help numbers

Find f g fg fg and f g and their domains f x 16 x g x x 3 Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find x Find the domain of x Enter your answer using interval notation

Find the derivative d d log 3x 2 7 2x 2 Jog 3

Find the inflection point of the function Hint g 0 does not exist g x 8x x x g x

The graph of y f x is shown to the right Graph y f x 6 Choose the graph of y f x 6 OA O 101 C Ay 10 JHHHHH STII 10 HIE X 10 HTT 10 o 57 OB OD Ay 10 10 10 X 10 TONTT 10 5 o 10 8 6 4 f x Ay 10 8 6 2 2 6 8 10 K 6 8 10

Find fx fy fx 4 5 and fy 3 3 for the following equation f x y x y fx Type an exact answer using radicals as needed fy Type an exact answer using radicals as needed fx 4 5 Type an exact answer using radicals as needed fy 3 3 Type an exact answer using radicals as needed

Find the indicated derivative for the function f x for f x 6x7 7x 2x 7

Find f f and f The symbol is the Greek letter lambda f x y 2 x y 2 4x 5y 14 X K 11 f

sin 10 221 221 0 0 2TT How do I find the angle of this The answer should be 317 7 but I can t figure out how to get it

Find the derivative d dx d dx log2 5x 6 log2 5x 6

A rancher plans to fence in a rectangular corral adjacent to a river for a herd of cattle The corral must contain 281 250 square meters in order to provide enough grass or the herd No fencing is required along the river Use calculus to determine the dimensions and of the corral that will require the least amount of fencing How much fencing is required 2 The length of the shorter side of the optimal corral is The length of the longer side of the optimal corral is Y 20 meters long meters long

Kayla is viewing a video presentation in a large conference room The presentation is being projected onto a large wall The lower edge of the presentation viewing window is 8 feet above Kayla s eye level The height of the presentation viewing window is 40 feet How far away from the wall should Kayla stand in order to obtain the maximum viewing angle for the presentation Presentation I

In the graph of y csc 2x e what is the coordinates of the SECOND point A 3 e B 3 e c 3 e D 3 e E NO correct choices

The population of Linz County can be modeled by y 684t 48700 where t is the number of years after 1960 Use the model to estimate the population of Linz County in the year 2020

The graph of y cos x is vertically stretched by a factor of 14 shifted a distance of 5 units to the left and translated 4 units upward Find a formula for the function whose graph is the resulting graph f x

2 Let f x 1 x for x 0 00 and let g x tan x for x 1 2 1 2 Which of the following statement is truc d g x for x E 1 2 1 2 dx f x d f x g x 2x scc for x T 2 2 a C 2x tan x 1 x2 2 b c d f g x 2g x for x 1 2 1 2 f r g x sec x 1 x 2x tan x for x 1 2 1 2 e None of the above statements is truc

4 Suppose that f is a differentiable function on o co such that f x ax bx c for I 1 0 for some constants a b and c and f x 0 5 for x 1 Which of the following statements is false a c a 0 5 b If f 0 0 then f 0 2 c If f 0 2 then a 1 d If f 0 0 then f x f x 0 for x 1 1 e f is continuous at 0

Note For Part II Problems SHOW YOUR WORK TO GET THE POINTS 11 20 points Use Newton s method to find the zero of f x x 3 with zo 2 Perform four iterations

Find the linear approximation L x of the function f x 4 xata 0 L x Use L x to approximate the numbers 3 9 and 3 99 Round your answers to four decimal places 3 99 Use technology to graph and the tangent line in the same viewing window 10 15 2 4 D 5 5 10 15 20 25 30 x 2 1

dy dx y 8 log 2x Find dy dx Simplify your answer

Find the relative rate of change of f x at the indicated value of x f x 360 5x x 19 The relative rate of change of f x at x 19 is Type an integer or decimal rounded to three decimal places as needed

Find A the derivative of F x S x without using the product rule and B F x S x Note that the answer to part B is different from the answer to part A 6 4 F x x 1 S x x A The derivative of F x S x is

Find dy dx II dy dx y 9 In x 5log gx Type an exact answer

Replace with an expression that will make the equation valid d 4 3x 7 4 3x 6 dx The missing expression is

The graph of f is given below Sketch the graph of f 10 8 6 4 2 Clear All Draw 10 8 6 4 2 2 4 6 8 10 2 4 6 8 16 Ansics