Determine the maximums and minimums of the following function: x2 + 2y2 - xy
10. Let f(x1, x2, x3 6 22r3 Find stationary points and classify them as minimums or maximums ) xf+2%+3ag+ x1x22r123 0112r2
10. Let f(x1, x2, x3 6 22r3 Find stationary points and classify them as minimums or maximums ) xf+2%+3ag+ x1x22r123 0112r2
3.9. Problem*. (Section 9.1) The following problems concern maximums and minimums of collections of independent random variables. (a) Let Y.Y2, ..., Yn be independent exponential random variables with parameters 11, 12,..., In, respectively. Prove that E[min{Yı, Y2, ..., Yn}] < min{E[Y], E[Y2),..., E|Y.]} (b) Suppose that X1, X2, ..., X, are independent continuous random variables with uni- form distributions on (0,1). Compute E[min{X1, X2, ..., Xn}] and E[max{X1, X2,..., X.}]
Finding Absolute Maximums and Absolute Minimums. We are guided here by two theorems about extreme values of functions Theorem 1: Iff(x) is continuous on a closed interval [a, b], then f(x) has both an absolute minimum value, m, and an absolute maximum value, M. This means there are some numbers c and d with m = f(c) and M = f(d) and m s f(x) s M for each x in [a, b]. The theorem does not tell us where...
Sketch the functions shown below for the intervals indicated. Make sure values for maximums and minimums are clearly indicated. 0sts4 a). b), c). q(t) 2tu(t)- 2(t-1)u(t-1)-2(t-2)u(t-2)+ 2(t-3)u(t-3) g(t) = 2coszt u(t)-2 cost(t-2) u(t-2) q,(t) = 2δ(t-1)-8(t-2) 0sts4 0sts3 Write the expression for the following functions using the unit step notation y(t) 니 7 z(t)
1. Find any absolute maximums or minimums of f(x)=xV1 - X on (-1,1). Use calculus methods illustrated in your book and notes and show all work. Do not use a graph to justify your answer. 2. Evaluate the limits using calculus methods illustrated in your book and notes and show all work. Do not use a graph to justify your answer. a. liman 2-0*+sin(2x) tan(4x)
7. Use information from the derivatives of f(x) to help you gra Find all local maximums and minimums. f(x)x3-9x2 +80 80 50 30 201 10 -6 30 8. For the given cost function Cox)-2-100x+10.000, find: a) The cost of production level 10 b) The marginal cost function? c) The marginal cost at production level 10 d) The production level that will minimize the cost Math 148 Business Calculus Page 3
7. Use information from the derivatives of f(x) to help...
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the constraint glx.v) = -6x + 3y - 12. Find the optimal point of f(x,y) subject to the constraint g(x.). Enter the values of, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places y f(x,y) A-
Find the intervals where f(x) = xV(8 - x2) is increasing and decreasing. Identify any local minimums or maximums.
3. Consider the function f(x,y) = 4 + 2x - 3y - x2 + 2y2 - 3xy. a) (5 pts.) Calculate the partial derivative functions, and use them to calculate the gradient vector evaluated at c = b) (5 pts.) Write down the affine approximation to at the e given in a) /(x) = f(c)+ Vf(e)'(x - c) . Use it to calculate (1.1, 1.1). (Hint: it should be close to f(1.1, 1.1))
Question 7 Which of the following is an equation of an ellipse? X2 + 2y2 = 1 x2 + y2 = 1 O x²+2y3 = 1 x2 - 2y2 = 1 O Question 8 Which of the following is equivalent to 14x-1|<11? (You are not asked to solve the inequality.) 4x-1<11, or 4x - 1>- 11 -11<4x-1<11 O 4x-1<11 -11 > 4x - 1<11 Question 9 Which of the following is equivalent to logxy? logy - logx Iny - Inx...