Reference no: EM131038302
Calculus-
1. The average cast a(q) of producing q items is defined as the total cost C(q) divided by the number of Items, q, so a(q) = C(q)/q. Explain why the average tea Ls minimized when the marginal can Ls equal to the average cost In:
(a) mathematical terms
(b) economic terms.
2. The average cost per item to produce q items is given by a(q) = 0.01q2 - 0.6q + 13. for q> 0.
(a) What Is the total cost, C(q), of producing q goods?
(b) What is the minimum marginal cost? What is the practical interpretation of this result?
(c) At what production level is the average cost a minimum? What is the lowest avenge cost?
(d) Compute the marginal met at q = 30. How don this relate to your answer to pan (c)? Explain this relationship both analytically and in words.
3. Consider the function f(x) = x3 - 3x2.
(a) Find the equation of the derivative f'(x).
(b) Find the equation of the tangent to the graph of f at x = 2.
(c) Find the equation of the normal at x = 2. (The normal is the line perpendicular to the tangent).
(d) Sketch f(x),f'(x)', the tangent at x = 2. and the normal at x = 2. Label any critical points of f.
4. Find the derivatives of the following (Unction using the various rules for computing derivatives
(a) f(x) = x3 - 3x2 + 7x-6
(b) g(x) = x + √(x2 + 1/x2)
(c) r(t)=(t2 - t + 1)(5 + 2t - t3)
(d) q(s) = (2s - 7)5(3s + 1)6 (Factor the answer as much as possible.)
(e) w(z) = z2 + 8z + 1/z2 - 1
5. Find the global maxima and minima of the following functions over the stated interval.
(a) f(x) = 2x2 +6x +2 on [-1, 3].
(b) g(x) = x3 - x2 +12x - 7 on [-4, 4].