Suppose that the functions f and a and their derivatives with respect to a have the...
Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the given combination at the given value of x. x/t(x) g(x) f'(x) g'(x) 3 1 16 6 5 4 - 3 3 4 N f(x) g(x), X = 3 Select one: O A. 197 OB. 37 O C. 101 OD. 60 to the integral
3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and w(x)-g(f(x)) Use the graphs to find the indicated derivatives. If the indicated derivative does not exist, write "D.N.E." in the space provided. Be sure to include work that shows how you arrived at your answer. 20 a) u'3) b) v-4) c) wl) 3. Below you are given the graphs of the functions f and g. Suppose that: u(x)-f(g(x)), v(x)-f(x) g(x), and...
1. Derivatives practice: a. Find the marginal product of labor when F(x)-4KL (Take the derivative with respect to L b. Find the marginal product of capital when F(x)-4KL (Take the derivative with respect to Find the marginal product of labor when F(x) = 61K3 (Take the derivative with respect to L). c. d. Find the marginal product of labor when F(x) 61/2 K1/ (Take the derivative with e. Find the marginal product of labor when F(x) = 11/4K3/4 (Take the...
Find the first derivative with respect to the domain variable for the following functions. 4. f(x) = (x - 2)(x² + 2x +4)
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
(18) Let f and g be functions from R to R that have derivatives of al orders. Let h(k) denote the kth derivative of any function. Prove using the product rule for derivatives, the fact that and induction that k +1 k=0 (19) The Fibonacci numbers are defined recursively by Fn+2 = Fn+1 Prove that the number of subsets of { 1, 2, 3, . . . , n} containing no two successive integers is E, (20) Prove that 7n...
72 Partial Derivatives: Problem 16 Next Previous Problem List (1 point) Suppose the f(x, y) is a smooth function and that its partial derivatives have the values, f(0,-4) 5 and f,(0, -4) =-1. Given that f(0,-4) = 0, use this information to estimate the value of f(1,-3) Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation. Estimate of (integer value) f(1,-3) 72 Partial Derivatives:...
5. Suppose that we have f(x)e. Use derivatives to answer the following questions. Solutions based on graphical or numerical work will receive no credit. (a) (4pts) Find f"(), the second derivative of f(x) (b) (2 pts) Confirm that x =-1 is a critical point of f(x). (Evaluate f'(-1), and make a conclusion. (c) (4pts) Use the second derivative test to classify -1 as a local max. or a local min. If the second derivative test is inconclusive, then say so....
7. Suppose We have three functions f(x), g(x), and h(x), such that f(-2) = 7, 9(-2) = 3, h(-2) = 10, f'(-2) = -14, 5'(-2) = 0, and '(-2) = 100. What is the derivative of In [Chooker)] at x = -2? a)-16 b) -0.22 c) -16.5 d) -33.5 e) -3/4 8. What is the slope of the tangent line (dy/dx) at the point (1,0) to the curve given by the equation (78 + y) = (1 - 4y)? a)...
1. (20 points) Find derivatives of the following functions. (a) f(x) = 1012 (b) g(x) = (ln(x2 + 3)] (c) h(x) = Vx+V2 (d) y=et +e? – x-e