Tuesday

January 17, 2017
**Calculus **

Find the Riemann sum for f(x) = sin x over the interval [0, 2Ï€], where x0 = 0, x1 = Ï€/4, x2 = Ï€/3, x3 = Ï€, and x4 = 2Ï€, and where c1 = Ï€/6, c2 = Ï€/3, c3 = 2Ï€/3, and c4 = 3Ï€/2.

*Monday, November 7, 2016 by Nelson*

**pre-calculus**

Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt . The count in the bacteria culture was 900 after 20 minutes and 1600 after 30 minutes. (a) What was the initial size of the culture? (b) Find the population after 80 minutes. (c) How many ...

*Monday, November 7, 2016 by kevin*

**Calculus**

I apologize if this question is too much to ask on this site, but I am really confused. Any help would be greatly appreciated. The famous formula shown below is called Eulerâ€™s formula, after the Swiss mathematician Leonhard Euler (1707-1783). e^(a + bi) = e^(...

*Monday, November 7, 2016 by Sade*

**Calculus**

What is the absolute value of: 3 - 8i? A. 9 B. 64 C. âˆš55 D. âˆš73

*Monday, November 7, 2016 by Sade*

**Pre-Calculus**

What is the absolute value of: 3 - 8i? A. 9 B. 64 C. âˆš55 D. âˆš73

*Monday, November 7, 2016 by Sade*

**calculus**

Consider the function f(x) = e^sin(cos(x)) on the interval [0, 4Ï€] a) The critical points of f are at__________? [Hint: The range of the function cos(x) is [âˆ’1, 1]. What is the range of the function cos(cos(x))?] b) Local maxima are at ________? ...

*Monday, November 7, 2016 by Kevin Land*

**calculus**

Ola, I'm not understanding this question, any assistance? Thank you very much. Find the distance of the line y = 2x + 6 from the circle x^2 + y^2 = 0.5 Find the point of the line that is closest to the circle. [Hint: a point on the line is closest to the circle if it is ...

*Monday, November 7, 2016 by Kevin Land*

**calculus**

Hello there, assistance would be terrific, thank you very much. Consider the function f(x)= x^3 + 2x^2 + bx. a) The equation of the tangent line to the graph of this function at x = 1 is given by y = ? b) The tangent line intersects the x-axis at x = ? c) For what value(s) of ...

*Monday, November 7, 2016 by Kevin Land*

**Calculus**

f'(x)=sqrt(x)*sin(x) The first derivative of the f is given above. If f(0)=0, at what value of x does the function f attain its minimum value on the closed interval [0,10]?

*Monday, November 7, 2016 by Mike*

**Calculus**

Imagine making a tent in the shape of a pyramid. Assume we want the volume to be 2.2m3 to sleep two or three people. Draw a picture identifying all appropriate variables. The floor of the tent is cheaper material than the rest: assume that the material making up the dome of ...

*Sunday, November 6, 2016 by Cheyenne*

**Calc 1**

A rectangle has one side on the x-axis, one side on the y-axis, one vertex at the orgin ans one on the curve y = e^-3x , for x>(equal) 0. find the maximum area (using calculus)

*Sunday, November 6, 2016 by Melissa*

**Calculus**

A particle moves along the x-axis and its position for time t is greater than or equal to 0, is s (t)=cos(2t)+sec(t). When t=pi, the acceleration of the particle is

*Sunday, November 6, 2016 by Jessica*

**Calculus**

A continous function y=f(x) crosses x-axis at points x=-3,0,2,5. Use mean value theorem to show that function has three critical points? I am stuck in this question kindly help

*Sunday, November 6, 2016 by Asfand*

**calculus**

y'? 1.y=arctan(a+x/1-ax); a is constant 2.y=e^x-e^-x/e^x+e^-x

*Sunday, November 6, 2016 by skorge*

**Pre-Calculus**

Use the following vectors to answer the question. u: <-1,7> v: <6,4> What is the projection of u onto v?

*Saturday, November 5, 2016 by Sade*

**Calculus**

Given: u <-1, 7> and v <4, -3> What is the measure of the angle between them?

*Saturday, November 5, 2016 by Iris*

**Pre-Calculus**

Given: u <-1, 7> and v <4, -3> Find: (u â€¢ v)(u + v)

*Saturday, November 5, 2016 by Iris*

**Calculus **

Two sides of a triangle are 4 inches long. What should be the angle between these sides to make the area of the triangle as large as possible?

*Saturday, November 5, 2016 by kate *

**Calculus Reimann Sum**

Approximate âˆ«_-2^3(x+3)dx via the Riemann sum. Use the partition of five subintervals (of equal length), with the sample point barx_i being the right end point of the i-th interval. I attempted this problem and got -40/3, but it's not being accepted. I&#...

*Friday, November 4, 2016 by Anonymous*

**Calculus**

let a_i = 2^i 20 Find Î£ a_(i+1)-a_i i=1

*Friday, November 4, 2016 by Josh*

**Calculus - Special sum formulas**

Find the formula of n Î£ (j+3)(j-4) j=1 I have gotten to n(n+1)(2n+1)/6 - n(n+1)/2 - 12n How do I simplify it from there?

*Friday, November 4, 2016 by Jamie*

**Calculus - Special sum formulas**

Find a formula for Sum_{j=1}^n (j+3) (j-4) So far, I have foiled to j^2-j-12. Thus,Sum_{j=1}^n(j^2) - Sum_{j=1}^n(j) - Sum_{j=1}^n(12). From Special Sum formulas, I have gotten to n(n+1)(2n+1)/6 - n(n+1)/2 - 12n What do I do from here?

*Friday, November 4, 2016 by James*

**Calculus**

A particle is moving with acceleration a(t) = 24 t + 4. Its position at time t =0 is s(0) = 15 and its velocity at time t =0 is v(0) = 11. What is its position at time t = 9?

*Friday, November 4, 2016 by Sam*

**Calculus - Differential Equations**

Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6. So far, I have: 4 du = u^2 dt 4/u^2 du = dt -4/u = t+C I am unsure what to do from this point...

*Friday, November 4, 2016 by Abby*

**Calculus - Falling Body Problem**

Near the surface of the earth, the acceleration of a falling body due to gravity is 32 feet per second per second, provided that air resistance is neglected. If an object is thrown upward from and initial height of 3000 feet with a velocity of 75 feet per second, find its ...

*Friday, November 4, 2016 by Jamie*

**Calculus - Differential Equations**

Use separation of variables to find the solution to the differential equation: 4 (du/dt) = u^2, subject to the initial condition u(0)=6.

*Friday, November 4, 2016 by James*

**Calculus**

Find the xy-equation of the curve that passes through (-2, -2) and whose slope at any point on the curve is equal to 5 times the x-coordinate of that point

*Friday, November 4, 2016 by James*

**Calculus**

An offshore oil well is 4 kilometers off the coast. The refinery is 5 kilometers down the coast (see figure). Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?

*Thursday, November 3, 2016 by Kurfy*

**calculus**

Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height T that is .3 times the width w of the rectangle If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter. h = w =

*Thursday, November 3, 2016 by diandra*

**Calculus **

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that ...

*Thursday, November 3, 2016 by Emily*

**Calculus**

Sketch the given region R and then find its area. R is the region bounded by the curve y=1/x^2 and the lines y=x and y=x/8.

*Thursday, November 3, 2016 by Anna Kirakosyan*

**Calculus **

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 1600 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that ...

*Thursday, November 3, 2016 by Emily*

**calculus**

Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to overÂ come the centrifugal force, the road is banked at an angle of magnitude 0 from the horizontal. The banking angle must satisfy the equation rg tan 0 = v^2 ...

*Thursday, November 3, 2016 by Brian*

**calculus**

A patrol car is parked 50 feet from a long warehouse The light on the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes the folÂ lowing angles with the line perpendicular from the light to the wall...

*Thursday, November 3, 2016 by Brian*

**Calculus**

If f(x) = 2xsqrt(x-6), what is the value of (f^-1)(40)?

*Wednesday, November 2, 2016 by Anonymous*

**calculus**

A point is moving along the graph of y = x2 so that dx/dt is 2 centimeters per minute. Find dy/dt when (a)x = 0 and (b)x = 3.

*Wednesday, November 2, 2016 by Brian*

**Calculus**

All edges of a cube are expanding at the rate of 3 centimeters per second. How fast is the volume changÂ ing when each edge is (a) 1 centimeter and (b) 10 centimeters?

*Wednesday, November 2, 2016 by Brian*

**calculus**

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approxÂ imately three times the altitude. At what rate is the height of the pile changing when it is ...

*Wednesday, November 2, 2016 by Brian*

**Calculus**

A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 1 foot and (b) 2 feet?

*Wednesday, November 2, 2016 by Brian*

**Calculus**

Find the dot product of: <-1, 7> and <2, Â¾>.

*Wednesday, November 2, 2016 by Iris*

**Calculus**

A plane traveling 500 mph (called airspeed) in the direction 120 degrees encounters a wind of 80 mph in the direction of 45 degrees. What is the resultant direction of the plane (in degrees)?

*Wednesday, November 2, 2016 by Sade*

**Calculus**

Given ||v|| = 5 theta=30 degrees, write the vector v.

*Wednesday, November 2, 2016 by Sade*

**Calculus**

What is the unit vector of v: <-6, -8>?

*Wednesday, November 2, 2016 by Iris*

**Calculus **

Find the particular solution that satisfies the differential equation and the initial conditions. F'(x) = 4x^2 f (-1)=3 F'(t)=10t-12t^3 f (3)=2

*Wednesday, November 2, 2016 by Anonymous*

**Calculus**

A 5ft tall person is walking toward a light 20ft off the ground at 8 ft/sec. What is the rate of change of the length of the persons shadow when they are 15ft away from the light? What is the speed of the tip of the shadow moving?

*Wednesday, November 2, 2016 by Ben*

**Calculus**

True or False If F(x) and G(x) are antiderivatives of f(x), then F(x)=G(x)+C If f'(x) = g(x) then integral g(x) dx = f(x) + C Integral f(x) * g(x)dx = integral f(x)dx * integral g(x)dx I have a feeling it's False True True

*Wednesday, November 2, 2016 by James*

**Calculus **

Find the particular solution that satisfies the differential equation and the initial conditions. f''(x) = x^2 f'(0) = 8, f(o)=4 f'(t) 10t - 12t^3, f(3) =2

*Tuesday, November 1, 2016 by Emily*

**Calculus**

Find the points on the lemniscate, given below, where the tangent is horizontal 2(x^2 + y^2)^2 = 49(x^2 âˆ’ y^2)

*Tuesday, November 1, 2016 by Asfand*

**Calculus**

Find dy/dx at the point (-3, 1) for the equation x = y^3-9y^2+5. A. -1/17 B. -1/13 C. -1/15 D. 1/17 E. 1/15 I posted this question before with a typo, but the point still doesn't appear to be on the graph of the function.

*Tuesday, November 1, 2016 by Anonymous*

**Calculus**

Find dy/dx at the point (-3, 1) for the equation x = y^3-9x^2+5.

*Tuesday, November 1, 2016 by Anonymous*

**pre calculus **

A rectangular parcel of land has an area of 4,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot?

*Tuesday, November 1, 2016 by Maya*

**calculus**

find the economical proportion between the radius and height of the cylindrical can to give the least dimensions of a metal that encloses vloume of 10cu.in

*Tuesday, November 1, 2016 by skorge*

**Calculus**

The measurement of the circumference of a circle is found to be 70 centimeters, with a possible error of 0.9 centimeter. a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) b) Estimate the maximum allowable percent ...

*Monday, October 31, 2016 by Kayla*

**Calculus**

The velocity of an object is given by v(t)=t(t^2-1)^(1/3) feet per second. Find the total number of feet traveled by the object in the time interval [0,3] seconds. (A)51/4 (B)34/3 (C)45/4 (D)51/8 (E)45/8

*Monday, October 31, 2016 by Mike*

**calculus **

indefinite integral : (sqrt(V^2sin^2(2pi/T*t))) dt

*Sunday, October 30, 2016 by byu*

**Calculus differentiable and continous identify**

1. Which of the above functions are not continuous where they are defined? Why? 2. Which of the above functions are not differentiable where they are defined? Why? Photo Link: goo.gl/photos/2RPU1dAWoKzUn4Pf8 For the first question, I said that graph F is not continuous because...

*Sunday, October 30, 2016 by Ray*

**Calculus AB**

Um I don't really understand these word problems so could someone help me please? 1) An object is thrown upward with an initial velocity of 5 m/s from an initial height of 40 m. Find the velocity of the object when it hits the ground. Assume that the acceleration of ...

*Sunday, October 30, 2016 by Annie*

**Calculus AB**

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point. Sketch the curve...

*Sunday, October 30, 2016 by Annie*

**Pre-Calculus**

Why do we need to use the sum/difference formulas to find exact values? Please explain.

*Sunday, October 30, 2016 by KW*

**Calculus AB**

Could someone please help me with this? Calculate the instantaneous rate of change of f <note: f(x)=(x-6)/(x+6)> at x=6.

*Sunday, October 30, 2016 by Annie*

**Calculus**

Use the limit process to find the area of the region between the graph of the function and the y-axis over the given y-interval. f(y) = 7y, 0 ≤ y ≤ 2

*Saturday, October 29, 2016 by Matt*

**Calculus**

Determine an upper/lower estimate for the area under the curve f(x) = cos x between x = 0 and x = pi/2 . Show how you arrive at this estimate. This is the question that my teacher wanted us to answer and I'm not sure how to even start the process. Should I use Reimann'...

*Saturday, October 29, 2016 by Mia *

**Business Calculus **

As the financial consultant to a classic auto dealership, you estimate that the total value (in dollars) of its collection of 1959 Chevrolets and Fords is given by the formula v = 306,000 + 1,000t2 (t ≥ 5) where t is the number of years from now. You anticipate a ...

*Friday, October 28, 2016 by Anonymous*

**Calculus**

Given the vectors u = <−3, 7> and v = <5,1>, find 3u + 2v.

*Friday, October 28, 2016 by Iris*

**Calculus**

Given the vectors u = <−3,7> and v = <5,1>, find -Â½ u. A. <-1,-4> B. <-4,-1> C. <3/2,-7/2> D. <-3/2,7/2>

*Friday, October 28, 2016 by Sade*

**Calculus**

Find d^2y/dx^2 in terms of x and y given that 8x + 6y^2 = 8. Use the original equation to simplify your answer. A. y'' = -(4/9y^3) B. y'' = -9y^3 C. y'' = -4y^3 D. y'' = -27y^3 E. y'' = -(8/27y^3)

*Friday, October 28, 2016 by Anonymous*

**Calculus I**

(Six pigpen problem). A 2 Ã— 3 array of six congruent rectangular pigpens (that all look the same from above) will be in the overall shape of a rectangle R. We may use 100 feet of fencing to form the boundaries of the pigpens. Find the dimensions for a single ...

*Friday, October 28, 2016 by Rebecca*

**Calculus**

How to derive cosh (3x) in terms of cosh (x) and sinh (x) ? Initially I start with 1/2 (e^3x+e^-3x) but I'm stuck from there because I don't know how to continue... :(

*Friday, October 28, 2016 by Matilda*

**calculus**

need help in below question. Thanks. A man runs round a circular track at a constant speed. Would like to know how to drawn locus of the points representing the magnitude â€˜dâ€™ of the displacement of the man from the starting position against ...

*Thursday, October 27, 2016 by peterlaw*

**ab calculus**

Air is being blown into a spherical balloon at the rate of 75 cm3/s. Determine the rate at which the radius of the balloon is increasing when the radius is 28 cm.

*Wednesday, October 26, 2016 by ron*

**calculus **

A car is traveling west at 67 mi./hr and a truck is traveling south at 59 mi./hr. Both are headed for the intersection of the two roads. At what rate are the car and truck approaching each other when the car is 0.2 mi. and the truck is 0.5 mi. from the intersection?

*Wednesday, October 26, 2016 by josh*

**Differential calculus**

Differentiate the following y=root(e^x)/x

*Wednesday, October 26, 2016 by Mohammed*

**Differential calculus with analytic geometry **

use implicit differentiation to find dy/dx. xy^2+4y^3=x-2y

*Wednesday, October 26, 2016 by Mohammed*

**Calculus**

Find the equation of the tangent line to the curve 2x^2y-3y^2=-11 at the point (2,-1).

*Wednesday, October 26, 2016 by Audrey*

**College Calculus**

If a ball is thrown vertically upward from the roof of 48 foot building with a velocity of 96 ft/sec, its height after t seconds is s(t)=48+96t−16t^2. What is the maximum height the ball reaches? What is the velocity of the ball when it hits the ground (height 0)?

*Wednesday, October 26, 2016 by Jaken *

**Calculus**

A particle moves according to the equation of motion s(t)=t^2-2t+3 where s(t) is measured in feet and t is measured in seconds. Find the total distance traveled in the 3 seconds.

*Wednesday, October 26, 2016 by Audrey*

**Calculus**

Starting at t=0, a particle moves along the x-axis so that its position at time t is given by x(t)=t^4-5t^2+2t. What are all values of t for which the particle is moving to the left? (A)0<t<0.913 (B)0.203<t<1.470 (C)0.414<t<0.913 (D)0.414<t<2.000 (E)...

*Wednesday, October 26, 2016 by Mike*

**Calculus**

Find the slope of x^2-16xy+y^2=1 at (1,1). Is this -1?

*Wednesday, October 26, 2016 by Anonymous*

**Calculus (AC)**

Steve, you've been an amazing help. Thank you so much. This is the last question I need checked. Solve ∜82 using differentials. I got 3.00926

*Wednesday, October 26, 2016 by Sarah*

**Calculus (answer check)**

The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches. (Use differentials to approximate the possible propagated error and the percent error. Propagated error= 1.6% Percent error= 4.6%

*Wednesday, October 26, 2016 by Sarah*

**Calculus **

The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches. Use differentials to approximate the possible propagated error in computing the area of the circle and find the percent error. I've gotten to 2Pi*16*.25 but don't know what to ...

*Tuesday, October 25, 2016 by Sam*

**Calculus**

The function f is given by f(x)=3x^2+1. What is the average value of f over the closed interval [1,3]? The answer I get is 12, but the book says it's 14. I don't understand why.

*Monday, October 24, 2016 by Mike*

**math calculus**

A poster is to contain 300 (cm square) of printed matter with margins 10cm at the top and bottom and 5cm at each side. Find the overall dimensions if the total area of the poster is minimum.

*Sunday, October 23, 2016 by Aquino,Vanessa Mae*

**Calculus**

Ship A is moving east at 20 miles per hour, while ship B is moving north at 15 miles per hour. At noon ship A was 5 miles east of an island, and ship B was 75 miles south of the island. At what rate is the distance of the ships changing at 1 pm?

*Sunday, October 23, 2016 by Allie*

**Math (Calculus)**

Determine if each of the following functions is in Big-O, is Big-Omega and is Big-Theta of x: (Could be multiple) a) f(x)=10 b) f(x)=3x+7 C) f(x)=x^2+x+1 d) f(x)=5log(x) e) f(x)=|x| f) f(x)=x/2 I'm in calc 1 and I have no idea what's it even asking me. Help? Thanks in ...

*Saturday, October 22, 2016 by Ray*

**Calculus**

An error in the measurement of the radius of a circle results in an error in the computation of its area. Find and interpret the sensitivity of area (a) of a circle to the measurement of radius, r, when the radius r=2 meters.

*Saturday, October 22, 2016 by jan*

**Calculus**

Can you please help me find the x and y intercepts of this equation. How do I solve this? y= x^2 √9-x^2

*Saturday, October 22, 2016 by Stephanie*

**CALCULUS**

if F(x) = f(xf(xf(x))),where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5,and f '(6) = 6,find F '(1).

*Saturday, October 22, 2016 by Gagan*

**calculus**

Union membership as a percentage of the labor force can be modeled by M(x) = 0.0003x3 − 0.066x2 + 4.64x − 81, where x is the number of years after 1900,and M is membership as a percentage of the labor force. a. Find the rate at which membership is changing in 1960...

*Friday, October 21, 2016 by lis*

**Math (Calculus)**

Determine if each of the following functions is in Big-O, is Big-Omega and is Big-Theta of x: (Could be multiple) a) f(x)=10 b) f(x)=3x+7 C) f(x)=x^2+x+1 d) f(x)=5log(x) e) f(x)=|x| f) f(x)=x/2 I'm in calc 1 and I have no idea what's it even asking me. Help? Thanks in ...

*Friday, October 21, 2016 by Ray*

**Calculus 2**

A spring has a natural length of 25 meters. A force of 12 newtons is required to stretch the spring to a length of 30 meters. How much work is done to stretch the spring from it's natural length to 40 meters? -I forgot to add the 40 meters part to my other question here is...

*Friday, October 21, 2016 by chase*

**calculus 2**

A spring has a natural length of 25 meters. A force of 12 newtons is required to stretch the spring to a length of 30 meters. How much work is done to stretch the spring from it's natural length?

*Friday, October 21, 2016 by chase*

**Calculus**

Let f be a function with second derivative given by f''(x)=sin(2x)-cos(4x). How many points of inflection does the graph of f have on the interval [0,10]? (A)Six (B)Seven (C)Eight (D)Ten (E)Thirteen

*Friday, October 21, 2016 by Mike*

**Calculus**

differentiate the given function, simplify your answer by leaving no negative or rational exponents. final answer should be in factored form where possible. y=(x^2 +2x)^3(x+2)

*Thursday, October 20, 2016 by matt*

**Calculus**

A nut store sells 200 bags of almonds per month at a price of $5 per bag. For every $0.20 decrease in the price, the store sells five more bags per month. Determine the marginal revenue when 120 bags are sold.

*Thursday, October 20, 2016 by Matt*

**Calculus**

f(x, y) = 3ycos x, 0 ≤ x ≤ 2π Finding the locla minima, maxima, and saddle points. Having difficulty as so far I have: Fx = -3ysinx Fy = 3cosx Fxx = -3ycosx Fyy = 0 Fxy = -3sinx I have set both Fx and Fy equal to 0 but am not too sure about the critical points...

*Wednesday, October 19, 2016 by OscarEE*

**Calculus**

A nut store sells 200 bags of almonds per month at a price of $5 per bag. For every $0.20 decrease in the price, the store sells five more bags per month. Determine the marginal revenue when 120 bags are sold.

*Wednesday, October 19, 2016 by matt*

**Calculus**

The demand function for a bottle of hand lotion is p(x)=0.78+0.0003x, where x is the number of bottles sold and p is the price, in dollars. The cost function is c(x)=480-0.32x+0.0005x^2. Find the marginal profit when 700 bottles of hand lotion are sold.

*Wednesday, October 19, 2016 by matt*

**Calculus**

Determine the coordinates of the point on the graph of f(x)=3x^2-7x+4 where the tangent line is parallel to the line 5x+y=3

*Wednesday, October 19, 2016 by matt*

**Calculus**

find the point, (c,f(c)), on f(x)=x^2 in the interval 0≤X≤4, such that f'(c) equals the average rate of change over that interval.

*Wednesday, October 19, 2016 by matt*