6. If f(x) = x³ - x, find and interpret f"(x)

Q: A stone is thrown vertically upward with a velocity of 40 feet per second from the top of a tower 20...

A:

Q: Use the given functions to find each of the following and their respective domains. Do not try to si...

A:

Q: 13) y = 4c°(sin 0 – cos ) A) 8e® sin e B) 0 ) 4e0(sin e – cos e) + 4e® D) 8e®(sin 0 – cos 0) 14) y =...

A:

Q: S(x5 + 10)®x*dx 4 X.

A:

Q: It is known that the population of a certain country at time t is proportional to the people living ...

A:

Q: For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the gener...

A: 46. h,k=-2,-1, x,y=-4,348. h,k=2,3, x,y=5,12

Q: Determine the general solution of the given differential equation

A: Rewrite the equation in standard form. And solve it 

Q: If tan x = what is the value of cot 2x? o 1 13 o 5 o 12 - O 13

A: Find value of cot2x

Q: 4 7 7x+25 - Error Analysis. A classmate said that the sum of r²-9 and x+3 is -9 -

A: Given,            The sum of 4x2-9 and 7x+3 is 7x+25x2-9.To find : What mistake did your classmate m...

Q: Consider the given vector equation. r(t) = 3 sin(t)i + 4 cos(t)j (a) Find r'(t). r'(c) = (b) Sketch ...

A: Solution of question is written in step2.

Q: Find the volume of the solid with the given base and cross sections. The base is the circle x? + y? ...

A:

Q: Use integration by parts to evaluate the integral. sin(In(5x))dx

A:

Q: Given: cos 0 e is in QI. What is the value of cos 260? 4 6. o 1 3 O 4 6. 6.

A: We have to find value of cos(2theta).  

Q: Evaluate the integral of * 4xV16 x2 using the new variable. а. 2/3 оБ. 256/3 c. 255/3 O d. 15/3

A:

Q: Which Riemann sum represents the illustration shown? AY 32+ 24+ 16+ 8+ X 1 2 3 4 4 o 1 2 2x,² i=1 3 ...

A: The points in the curves can be identified as: x=2, y=8 x=4, y=32 So, the curve represents the funct...

Q: find the dot product of a vector function with itself. r(t) is a curve and the magnitude of r(t)=pi ...

A: Let  u = a i^ +b j^ be a vector functionthe dot product of u with itself is given byu·u = a i^ +b j·...

Q: Write a full solution  Let consider the following function: ?(?) = 2(? + 1)^2  −8.  A) Find the x-...

A:

Q: Compute the given integral. 5x°e3 dx %3D +C

A:

Q: x²y' + xy = 2 + x²

A:

Q: One of the parts in the proposed design of a gadget is a tapered cylinder. It is made by decreasing ...

A: To solve the equation for L, 

Q: (IV) Give the standard form for the 3D TANGENT LINE to the associated curve: r (t) = ( 2 sin (t), 3 ...

A:

Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty o...

A: We have to find P value and point.

Q: Which of the following statements are true? Statement 1: Angles of 5° and-365° are coterminal. State...

A: To write the statements which are true. 

Q: Let cH)=LE?, t,6">, a) T(1) 5) K1)

A:

Q: QUESTION 1 a) Find the interval(s) on which the curve f(x)= x°(x- 3) is increasing and/or decreasing...

A:

Q: Suppose that g is a function that is differentiable at x = 4 and that g(4) = -2 and g' (4) = 1. Find...

A: We are asked to find the value of h'(4)

Q: If f(x) 3. find f'(4).

A:

Q: 8²z 8. If z = x + y Inxy, show that x- 8 z + x² 8²z 8y² 8x8y

A:

Q: Find the volume of the wedge in the figure by integrating the area of vertical cross sections. Assum...

A: Solution: a=6, b=3, and c=4

Q: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by a vector equation ...

A: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by a vector equation ...

Q: Find the oblique asymptote. 7 - x3 f(x) = 2x2 7-x3 2x2 y =

A:

Q: 3. (D³ + 2D² + D + 2)y = 0

A: The given differential equation is; (D3+2D2+D+2)y=0  

Q: Find the slope of the curve at the indicated point. 3 25) y=8+ X -x=7 A) m = B) m =- 75 C) m = D) m ...

A:

Q: 7. In a certain country, the number of people (in millions) using their mobile phones to check email...

A: Given query is to find the derivative of the function at different points.

Q: Find the average value of f(x) = x² /57 + x³ 3 on the interval [0,4]. favg %3D Report answers accura...

A: Follow the procedure given below. 

Q: Write an equation of the tangent line to the curve f (x) = 2// + 3x at the point (4, f (4)). Upload ...

A: Here, the given equation of the curve is: f(x)=2x+3x To find the slope and the equation of the tange...

Q: If is the diameter of the circle with A = (-2,6) and B = (5, 4), then the center of the circle is at...

A: AB is the diameter of the circle with A=-2,6 and B=5,4

Q: Given functions m(x) = = VE and h(z) = z - 4, state the domains of the following functions using %3D...

A:

Q: -7 Let f(x) 7xVI + f'(x)

A:

Q: Find dy/dt. 9) y = cos (rt - 20) A) -7n sinº(nt – 20) C) 7 cos (zt - 20) B) -7n cos(nt – 20) sin(7tt...

A:

Q: For the functions f(x)=-10x+7 construct and simplify the difference quotient f(x+h)−f(x) \ h The di...

A:

Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4 -2(...

A: Given:        y= x+12x2+1-3

Q: Find (f -1)(-2) for f(x)=3x+8. Round your answer to two decimals.

A:

Q: x = 3.61 E-6 (A) What is the equivalent decimal number? O-3.61 0.000361 O0.0000361 O0.00000361 (B) R...

A:

Q: 5.Find the area of the surface generated by revolving the given curve about the y-axis. x= 19- y, - ...

A:

Q: O Question 9 > Rewrite this number in appropriate scientific notation: 27, 050 answer =

A: Given, number is 27050

Q: 8x+5<15

A:

Q: use the vortex (h,k) and a point on the graph (x,y) to find the general form of the equation of the ...

A:

Q: Limits a. Find the limit: lim (x,y)→(1,1) (xy - y - 2x + 2) / (x - 1) . b. Show that lim (x,y)→(0...

A: Find limits   a. Find the limit: lim (x,y)→(1,1) (xy - y - 2x + 2) / (x - 1).b. Show that lim (x,y)→...

Q: Sin zt 2 2 7o47 mous

A: