Math

CalculusQ&A Librarypossible area? (Hint: First express y as a function of x, and then express A as a function of x.)losed area A. What is the largestthe2is11. Find the point on the graph of y x3 that is closest to the point (4, 0).12. An open box with a rectangular base is to be constructed from a rectangular piece of cardboard16 inches wide and 21 inches long by cutting a square from each corner and then bending upthe resulting sides. Find the size of the corner square that will produce a box having the largestpossible volume.13. A metal cylindrical container with an open top is to hold 8 cubic foot. Find the dimensions thatrequire the least amount of material.14. Use the Extreme Value Theorem (EVT) to find the absolute maximum and absolute minimumvalues of the function f(x)-x+ cos 2x on the interval 0,+ 1satisfies the hypotheses of the Mean Value Theorem on thex-115. Show that the function f(x) =interval -2,-1, and then find a number c in (-2,-1) that satisfies its conclusion.Use Newton's Method to approximate the-zero iffplaces.t5x3, aceurate to 3 deeimalA particle is moving with the given data. Find the position of the particle:a(t) = sint + 3cost, s(0) = 0, v(0) = 237Question

Asked Nov 12, 2019

3 views

I need help solving and understanding how to solve number 15. Thank you

Step 1

As per the definition, the Mean Value Theorem is defined for a point “c” between two endpoints “a” and “b” such that the tangent at the point [c,f(c)] is parallel to the secants passing through the two endpoints a and b.

Step 2

For the application of the Mean Value Theorem, the following conditions must be fulfilled.

**(1) Function f must be continuous in [a,b]**

**(2) Function f must be differential in (a,b)**

**If both the condition satisfies then, there exists a single point c and the value of f '(c)** **can be calculated.**

Step 3

First of all,** checking for continuity of f(x) in [-2,-1].**

**We know that polynomial equations are continuous functions.**

**Also, (x-1) = 0 at x = 1 and 1 does not lie in (-2,-1) therefore, f(x) is continuous in [-2,-1]. **

**To check differentiability, differentiate f(x) w.r.t. x**

**As (x...**

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: The problem is to put a "roof" of side s on an attic room of height h this is possible 2 and width b...

A: Click to see the answer

Q: 2,5 Given f(z, y) sin(x + y) where 2s 5t. Find f.(ar(s, t), y(s, t)) f(x(s, t), y(s, t)) =| Note: Th...

A: It is given that f (x, y) = sin (x + y) where x = s2t5 and y = 2s–5t.

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the functi...

A: Click to see the answer

Q: Identify the equation without applying a rotation of axes. 4x2-8xy+4y2-3x+6=0

A: Given, function is

Q: Simplify the expression. (−3ab4)(5ab−3)

A: Given:

Q: Find the standard form of the equation of the parabola using the information given. Focus:(0,13); D...

A: Given: Focus:(0,13); Directrix: y = -13

Q: Use cylindrical coordinates to find the volume of the solid that lies within the sphere x^2+y^2+z^2=...

A: Click to see the answer

Q: Can i get help step by step with this problem?

A: The given integral is

Q: Evaluate the integral and check your answer by differentiating: Hint: Add C to your answer. ∫[(5sin(...

A: Given,