Question
17. Let f(x) = (x - 3)-2. Show that there is no value of c
in (1, 4) such that f(4) - f(1) f'(c)(4 - 1). Why does
this not contradict the Mean Value Theorem?
Expand
Transcribed Image Text

17. Let f(x) = (x - 3)-2. Show that there is no value of c in (1, 4) such that f(4) - f(1) f'(c)(4 - 1). Why does this not contradict the Mean Value Theorem?

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point...

A: Consider the given curves and points.

Q: 7. According to a simplified economic model, the purchasing power of 1 dollar in the 2000t is equal ...

A: 2000+t=2020So, 20 years.

Q: Find the Taylor polynomial of degree 2 centered at (1, 2) for thefunction f(x, y) = 1/(xy)

A: Definition:

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 < 0 < 2n, and 0 s p n.) (0, 2 3, 2) ...

A: Formula for the converting rectangular coordinates to spherical coordinates.

Q: 4. Use the properties of logarith ms to rewrite each expression as the logarithm of a single express...

A: We know that,

Q: FInd the diemsions of a rectangular box, open at the top, having volume 727cm^3, and requiring the l...

A: Let the length, breadth and height of the box be denoted by a, b and h respectively, thenV=a × b × h...

Q: solve the equation 2cos(x+   7π/4)=√3 giving the exact solution which lie in [0,2π)

A: Divide by 2.

Q: Finding a Polynomial Find a third degree polynomia p(x) that is tangent to the line y = 14x - 13 at ...

A: Let p(x) = ax^3 + bx^2 + cx + dThis passes through (1,1) and (-1,-3) . For (1,1),  x=1 and y=1. For ...

Q: If the figure is the graph of the derivative f', answer the following: Where do points the points of...

A: Point of inflection occur at f"=0That is (f')'=0Means we have to find where the graph of f' takes tu...

Q: A piece of wire of length 63 is cut, and the resulting tow pieces are formed to make a circle and a ...

A: The total length of the wire is 63.Let x be the length of the wire cut for the circle.Then, 63-x is ...

Q: for this problem in the answer it says, cos^-1 (1/2)= pi/3,-pi/3. Why is that? Why did they go count...

A: According to question

Q: Match the blue graph of each function to the black graph of its derivative by writing the letter (A,...

A: Consider the first function:

Q: A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let ...

A: To find the number of units that should be produced at each location to minimize the cost.

Q: find the derivative 1).f(x)=X^3(X^4/3-1)                                                            ...

A: 1)

Q: f(x)-f(a) a. Use the definition mtan = lim to find the slope of the line tangent to the graph of f a...

A: Part (a) P(-3, 2) = [a, f(a)]Hence, a = -3, f(a) = 2Please see the whiteboard for the calculation of...

Q: Express the given quantity as a single logarithm. 2)2 In(x 2)7In x - In(x2 +

A: Let the given expression is:

Q: 51 and 52 Find dy/da and d2y/dx. For which values of t is the parametric curve concave upward? 51. t...

A: Given,

Q: The population (in millions) of the United States between 1970 and 2010 can be modeled as p(x) = 20...

A: Consider the given information:

Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) wit...

A: The position vector,

Q: 5 5 find sec(0) 12 and tan(e) 13 If sin(0)

A: Given,

Q: If xy + ey = e, find the value of yn at the point where x = 0.

A:  xy + ey = eWhen x = 0,  ey = e = e1Hence, y = 1

Q: Linear Approximate the change in the lateral surface area (excluding the area of the base) of a righ...

A: We have

Q: Given that the graph of f passes through the point (1,6) and that the slope of its tangent at (x, f(...

A: Given that the slope of the tangent at (x, f(x)) is 2x + 1.That is,

Q: Exercise 3: Find A and B given that the derivative f'(r) is everywhere continuous, and Aa2 Bx 2, x<2...

A: The function f(x) whose derivative is everywhere continuous is given by,

Q: f(x)=(4x^2)/[(x^2)−4].  Calculate the first derivative of f. Find the critical numbers of f, where i...

A: The given function is,

Q: Sketch the graph of a functionf having the following characteristics f(2) f(4) 0 f(x)0 if x > 3 f(3)...

A: First point represents the the x-intercepts. Second and fourth point is telling that the graph is in...

Q: Find the derivative of the function. f(x) = (2x − 3)4(x2 + x + 1)5

A: Given function is

Q: dy Given the equation below, find 36542yys = 41 dy da

A: We are given,

Q: Logarithmic Differentiation of (ln x)^x^2

A: Given expression

Q: -x2 The demand function for a product is p D(x) = 300e200 revenue. Show all of your work to prove it...

A: We know that Revenue function is given by

Q: An investment of $9,000 earns interest at an annual rate of 6.5% compounded continuously. Complete A...

A: Use the following formula,

Q: Does the series ∞ ∑(cos(πn))/n(squareroot(n)) n=1 converge​ absolutely, converge​ conditionally, or​...

A: Consider the given series,

Q: 7 If sin(0) 7 find sec(e) 24 and tan(0) 25

A: From the given information:

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: h(t) f(x, y), where f is differentiable, ax = g(t), and y Suppose z - 4, h' (6) 6, f2(8, If g(6) 8, ...

A: We are given that z = f(x, y), where f is differentiable, x = g(t), and y = h(t).

Q: Find dy/dx.x = t sin(t)y = t2 + 3t

A: Click to see the answer

Q: Express -x 2dx as aumit X eSS OF ngnt -hard Riemann Sums las the definition Of the indlefmite T cuva...

A: Given integral

Q: 4. Find the area that lies inside the curve r = 4 cos and outside the curve r = 2.

A: Given, curves are

Q: I can't find the tangential component of the acceleration

A: The given position vector is,

Q: Use logarithmic differentiation to find the derivative of the following function: y = (x - 1 / x4 + ...

A: Apply ln on both sides and simplify using properties of logarithm. 

Q: 10 0 x 2 et where x thousand lipsticks were sold per week at a price of p dollars each. At what pric...

A: Given:

Q: I am very confused on these two problems and I have homework due in 30 minutes.

A: Both problems concern finding deriviatives of functions ,using standard rules of differentiation

Q: I need help with question 21 in Section 3.11, page 264, of the James Stewart Calculus Eighth Edition...

A: Given,

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Click to see the answer

Q: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a spher...

A: Let r be the radius of the cylinder and h be the height of the cylinderR is the radius of the sphere...

Q: Optimization: A family wants to build a fence in their backyard for their dogs. If they can only aff...

A: Click to see the answer

Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: Find an equation of the tangent line to the curve at the given point. y = 5ex cos(x),    (0, 5)

A: To find the equation of the tangent line at the point (0, 5) to the curve given below.

Q: 49. Let f(t) be the temperature at time t where you live and suppose that at time t 3 you feel uncom...

A: a) f'(3)=2, f"(3)=4f'(3) &gt; 0 , so the temperature f(t) is  increasing at x=3f"(3)&gt;0 implies at...

Q: Consider the following.x = 1 + t2y = t2 + t3 (a) Find the following.(dy)/(dx) = (d^2y)/(dx^2) = (b) ...

A: Click to see the answer