10. Suppose that we are given the following information about the functions f and its derivatives;...
8. Suppose that we are given the following information about the functions f, g, h and k and their derivatives; • f(1) = 3 • f'(1) = 2 • g(1) = 4 • g'(1) = -2 • h(1) = 9 . h'(1) = -1 k(1) = 10 • k'(1) = -3 (e) (5 points) Set F(x) = log2[f(x) + g(x)]. Compute F'(1). (f) (5 points) Set F(T) = log: [f(r)g(r)h(r)k(r)]. Compute F'(1).
I cannot figure out the first
set of critical points and classifications.
(1 point) The following table gives values of the differentiable function y = f(x). X 0 1 2 3 4 5 6 7 8 9 10 y 1 -1 -3 -2 1-1 -2 123 5 Estimate the x-values of critical points of f(x) on the interval 0<x< 10. Classify each critical point as a local maximum, local minimum, or neither. (Enter your critical points as comma-separated xvalue,classification pairs....
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
For easy reference, f(z)- e- and its derivatives ()-2r(r-1)e 2r(r-1) 4r -8r +2 (x)-e(Az-8r+2)- and (c) Find lim (3) What is the horizontal asymptote? (d) Find the local max, local min, and/or inflection points, if they exist. You may use decimals (round to three decimal places) for your answers. (3) (e) Sketch the graph of f. Clearly label or state the points corresponding to the inter- cepts, asymptotes, local maxima and minima, and inflection points (if they exist). (6) 2...
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
help ASAP for my test
Suppose we are investigating max./min. behavior of a function (1). We intend using the first derivative test, and have gleaned the following information in preparation for applying the test. Interval Test value Sign behavior of f'() of !") of (2) 7-20,-2) f'(-10) = -0.5 (-2,0) f'(-1) = -3 (0,2) SO = 2 + (2,00) f'(5) <0 Apply the first derivative using the information in the table to select the appropriate conclusion for each critical point....
(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...
If 3.80 fig: [a,b] → R 2 Alonspiciens differentiable functions and we suppose Fca) = f(b) =. The wronskien of these a functions is the function TW Cf. g): [a, b] R defined by wCfg) () = det (FX) 906) -F68) g'(x)=9(x)}f'(X) (f'(x) g(x)) If W (f, g) (x) #0 for all x E [a,b], show that it exist a c E Ca,b) such that g (c) = 0.
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x