Optimization

Please see the attached file for full problem description. --- Problem 1 In deciding whether to set up a new manufacturing plant, company analysts have decided that a linear function is a reasonable estimation for the total cost C(x) to produce x items. They estimate the cost to produce 10,000 items as $547,500 and the cos ...continues

Minimization of a triangle area

Find the altitude to the base of an isoceles triangle with a side length of 4, such that the area of the triangle is maximal.

partial derivative question

I am taking a course by distance, and my professor provided an example of how to create a Hessian matrix using partial derivatives. He gave another example that just had the solution for us to try on our own. I think that I am somehow not taking the second order partial derivative right. The attached file has the professor ...continues

Calculus

Let f be the function whose graph goes through point (3,6) and whose derivative is given by f'(x) = (1+e^(x))/(x^2) a) write the equation of the line tangent to the graph of f at x=3 and use it to approximate f(3.1) b) Use Euler's method, starting at x=3 with a step size of .05 to approximate f(3.1). Use f'' to explain wh ...continues

It is a short description for finding the higher order derivatives of the function f(x)= (2^2^x)+1.It represents a Fermat Number when x is a positive integer. Find the higher order derivative of the function f(x) = [2^(2^x)] + 1.

Differential Calculus Fermat Numbers Higher Order Derivatives of f(x) = [2^(2^x)] + 1 The function f(x) = [2^(2^x)] + 1 represents Fermat numbers when x = 1,2,3,… Find the higher order derivative of the function f(x) = [2^(2^x)] + 1 ...continues

Differentiate the following...

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Integrate

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Integrate the following

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Going from First to Second Derivative

I have a first derivative and a second derivative, how do you get from the first to the second, I can't solve it. Please see the attached file for the fully formatted problems. M'(t) = pe^t/(1 - t^tq)^2 M''(t) = pe^t(1 + qe^t)/(1 - (e^t)q)^3

Double Integral : Horizontal and Vertical Simple Methods

I have managed to evaluate the double integral using the horizontal simple method, and answer 63. But when I reverse the order (vertical simple method) I cannot reach the same answer of 63, I get 65. 1) Evaluate the double integral of f(x,y)=x+4y^2 over the triangular region with vertices (-2,2) (4,2) & (1,-1) Check that r ...continues