# possible 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) = 237

Question
3 views

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

check_circle

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...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in