Differentiation Questions and Answers

Graph the given system of inequalities Choose the correct answer below O A 6 O C 6 x 2y 2 x 2y 2 6 x 2y 2 6 x 2y 2 OB x 2y 2 6 O D 6 6 x 2y 2 No Solution 6 4 2 6 4 2 2 4 6 2 N 4 A

Question 5 10 points The length L in cm of a pendulum is slowly decreasing at the rate of 0 100 cm s What is the time rate of change of the period 7 in s of the pendulum when L 16 0 cm if the equation relating the period and length is T L 245 T Paragraph E BI U A V OB 0 v I

Question 3 10 points Find the second derivative of the given function for the given value of x W a y 3x 3 2 b 11 X y 3 1 2x Paragraph v BIU A E E 00 0 v

Find dy dx in the following implicit function x x y x y Paragraph V BIU A v 11 00 Ins

Based on the ordered pairs seen in the table make a conjecture about whether the function f is even odd or neither even nor odd The function is odd odd neither even nor odd even BEX C because f x is equal to f x X 3 2 1 0 1 2 3 f x 10 5 4 0 4 5 10

Write the slope intercept form of the line that passes through the given point with slope m Do not use a calculator Through 6 8 m 5 The equation of the line is y Simplify your answer Type your answer in slope intercept form Use integers or fractions for any numbers in the expression

spe if defined of the line that passes through the given points 4 9 and 0 11 Find the slope of the line Select the correct choice below and fill in the answer box if necessary Type an integer or a fraction OA The slope of the line is B The slope is undefined

Select the correct choice below and fill in the answer box OA The equation of the line is OB The equation of the line is y

A mass on a spring vibrates horizontally on a smooth level surface as shown in the figure Its equation of motion is x c 8 sin t where t is measured in seconds and x In centimeters Equilibrium position t x a Find the velocity and acceleration at time t v t X In what direction is the mass moving at that time O b Find the position velocity and acceleration of the mass at time t 2 3

A graphing calculator is recommended Let f x 4e cos x a Find f x and f x f x b Check to see that your answers to part a are reasonable by graphing f f and f y y y y 150 125 100 75 50 25 R N K K X x 7 2 25 50 75 100 100 100 100 125 125 125 125 150 150 DO 150 KIN Describe the relationship between the three graphs Note that f 0 where f has a relative minimum or maximum and f 0 where f has a relative minimum or maximum Also note that f is negative when fis decreasing and f is negative when f is decreasing O Note that f 0 where f has a relative minimum or maximum and f 0 where f has a relative minimum or maximum Also note that f is negative when fis decreasing and f is negative when f is decreasing O Note that f 0 where f has a minimum and f 0 where f has a minimum Also note that f is positive when fis decreasing and f is positive when f is decreasing Note that f 0 where f has a relative minimum or maximum and f 0 where f has a relative minimum or maximum Also note that f is negative when fis decreasing and f is positive when f is decreasing Note that f 0 where f has a maximum and f 0 where f has a maximum Also note that f is positive when f is decreasin

Let the function f be defined by tan x 1 sec x a Use the Quotient Rule to differentiate the function f x f x f x b Simplify the expression for f x by writing it in terms of sin x and cos x and then find f x f x c Show that your answers to parts a and b are equivalent Yes O No Need Help Submit Answer 10 13 Deinal Read It Watch It

Evaluate the following integral 7 3 2 S 0 49 x2 7 3 2 S 0 T dx dx 49 x

Answer the following True False quiz Enter T or F 1 1 g 1 x g x 2 If f c 0 then f has either a local maximum or a local minimum at c 3 Continuous functions are differentiable 4 If f c 0 and f c 0 then f x has a local minimum at c 5 A continuous function on a closed interval a b attains a maximum and a minimum value in a b 6 If f x and g x are increasing on an interval I then f x g r is increasing on I 7 If f x e then f x 2e

Find the area of the given triangle Round your answer to the nearest tenth Do not round any intermediate computations 37 15 square units

1 Find the derivatives of the following functions A 5 pts f x x 4x 3x 1 B 5 pts g x sin x cos x 2 5 pts Given the function h z 5z 10z 1 5 compute h 2 3 5 pts Suppose that f 5 2 g 5 1 5 2 and g 5 3 Find h 5 where h x 3 f x 9

X 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 f x f x f x f x Derivative Function 4 3 2 1 0 1 2 3 4 Derivative Function 4 3 2 x 1 0 1 2 3 4 f x X 4 3 2 1 0 1 2 3 4 f x 4 3 2 1 0 1 2 3 4 f x f x f x Derivative Function X 4 3 2 1 0 1 2 3 4 Derivative Function X f x 3 2 1 0 1 2 3 4 f x

Determine the values of x for which the function is continuous function is not continuous the reason If the determine a x 6x 15 b x 2 x 7x

Find the derivative of y with respect to x y cos 7x 4

Question 8 Sketch a graph of f x 2x 4 2 5 4 3 2 1 5 4 3 2 1 T Question Help 1 2 3 4 5 Clear All Draw Video 1 1 2 3 4 V 5

Let f x 3 x If g x is the graph of f x shifted down 5 units and right 2 units write a formula for g x g x

Next question For the following exercise write a formula for the function obtained when the graph is shifted as described f x g x Get a similar question You can retry this question below is shifted down 2 units and to the left 6 units 2 6 2 X Question Help VIDEO D Post to forum

Which scatter plot indicates a perfect negative correlation A D The graph shows a scatter plot with a perfect negative correlation D B B E C F

Find an equation of the tangent line to the graph of f x ex where x 2 9 The equation of the tangent line is Type an equation Type your answer in slope intercept form Use integers or decimals for any numbers in the equation Round to two decimal places as needed

Question 7 Let f x 13x 12 x Question He

The table to the right shows teenage drug use in different countries Make a scatter plot for the given data Use the scatter plot to describe whether or not the variables appear to be related Make a scatter plot of the given data Choose the correct graph below O A 40 20 04 0 20 40 60 Marijuana 96 G OB 40 20 10 0 20 40 60 Marijuana Q Q OC 40 20 0 0 Country A B C D E F 20 40 60 Marijuana 96 Q Who Have Used Other Illegal Marijuana X 24 20 42 4 40 15 Drugs y 4 5 25 1 17 7 OD 40 20 0 Country G H 1 J K Who Have Used Other Illegal Drugs y 13 5 4 31 22 Marijuana X 23 6 6 50 34 0 20 40 60 Marijuana 96 Q

Differentiate the following function y x ex dy dx 11

f t 1 4 4 t 8

3 4 V r 1 1 r 3

JLO y x 5

4 If a snowball melts so that its surface area decreases at a rate of 1 cm min find the rate at which the diameter decreases when the diameter is 10 cm

3 Each side of a square is increasing at a rate of 6 cm s At what rate is the area of the square increasing when the area of the square is 16 cm

Evaluate each function ANSWER SHOULD BE A FRACTION OR MIXED NUMBER ANSWERS GIVEN AS A DECINMAL WILL BE COUNTED AS INCORRECT 5 f x 2 Find f 6 4 3 3

5 State the definition of the 6 Use the definition of the derivative i e the four step process to find the derivative of f x 7 4r

Determine whether the following pair of lines is parallel intersects at a single point or is skew If the lines are parallel determine whether they are the same line and thus intersect at all points If the lines intersect at a single point determine the point of intersection r 2 1 5 1 4 5 3 R 22 9 17 s 5 2 3 Select the correct choice below and if necessary fill in the answer boxes to complete your choice O A The lines intersect at the single point D Simplify your answers OB The lines are skew OC The lines are parallel OD The lines intersect at all points on the line r t

Suppose the value of y and the value of a vary together at a constant rate of change so that Ay 0 5 Ax and y 1 5 when x 3 a We are given that y 1 5 when 3 Plot a point on the graph to represent these values 8 7 6 S 4 2 1 3 2 1 1 y 1 2 3 4 5 6 7 8 Clear All Draw Dot x Ax 3 75 b Suppose the value of a varies from x 3 to z 6 75 i By how much did the value of a change Preview ii By how much did the value of y change over this interval of a Ay c What is the value of y when z 6 75 Preview Enter a mathematical expression more

Evaluate the integral S sec sec 5x tan 55x dx sec 5x tan 55x dx

Use any method to evaluate the integral cot 4x sec 4x cot 4x sec 4x dx dx 0

Evaluate the integral T S 2 3 70 sin 4x cos x dx I S 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expi 70 sin x cos x dx 4

Evaluate the integral Scos 3 cosx sin xdx 3 cos cosx sin xdx

Use L H pital s Rule possibly more than once to evaluate the following limit 102 112 lim 818 NE in the blank

A polynomial function has 3 real zeros and 4 non real zeros One of the real zeros has a multiplicity of 6 What is the degree of the polynomial 1 A 7 B 9 C 12 D 13

16 A stone is dropped into a lake creating a circular ripple that travels outward at a speed of 60 cm s Find the rate at which the area within the circle is increasing after a 1 s b 3 s and c 5 s What can you conclude

For the following quadratic function defined a use vertex formula to find the coordinates of the vertex a graph the function P x 4x 40x 98 AWN The vertex of the quadratic function is Type an ordered pair

4 g a a 1 h a 3a 4 Find 2 AX

6 Let f x 5x x f x 65x x 2 Question Help 5 35 4 2x x Video X

If f x 2 x x 5 x 3 find f x 2 1 x 5 x 3 2 x 3x 3 Find f 1 1 5 2 x X

The slope of the tangent line to the parabola y 2x 2x 5 at the point 3 29 is The equation of this tangent line can be written in the form y mx b where m is and where b is Question Help Video

If f x 7 then f x T

50x7 25x6 20 5x Type your answer without negative exponents Simplify completely Find the derivative of

Find the derivative of 4x 8 2x 6