How do i solve this? Let f(z) = +1 3 Where does f have critical points?....
I found that the critical numbers do not exist. How do I solve this? 6. Let f(x) = 2x. Then, f'(x) = 18 +2,and f"(x) = 4*12 - (9-x)? (9-x2) (a) Use a number line to demonstrate where ſ is increasing/decreasing. Label it carefully. (b) Use a number line to indicate the concavity of f. Label it carefully. (c) Compute lim 2x (d) List any intercepts and/or asymptotes for f. (e) Using all of the information above, carefully sketch a...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1, f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the data point (0, 3), find a Newton form for the Lagrange polynomial interpolating all 5 data points. 3. (25 pts) Let (r,, f()), 0,3, be data...
1. (20 points) Let C be any contour from z = -i to z = i, which has positive real part except at its end points. Then, consider the following branch of the power function zi+l; f(3) = 2l+i (1=> 0, < arg z < Now, evaluate the integral Sc f(z)dz as follows: (a) (5 points) First, explain why f(z) does not have an antiderivative on C, but why the integral can still be evaluated. (b) (5 points) Then, find...
sin (3) + sin (2-1) sina) 1. (10+7 points) Let f(z)= =1 +... (a) Does the series converge uniformly to f(x) on R? Is f() continuous? Is f(x) differentiable? (b) Calculate f(x) (i.e. write an explicit formula for f(x)).
14. If y =f(z) is a continuous function in a neighborhood around f'(c) = 0, does there have to be a local extrema on the graph of u = f(x) at x = c. 15. If/"(z) =-4(-7)2(z + 1) and the domain of f(x) is all real numbers, determine where f(x) is concave up, concave down and find any r-values of inflection points. 14. If y =f(z) is a continuous function in a neighborhood around f'(c) = 0, does there...
Help! Please do both of them with detailed explanation Find and classify the critical points of z- 28) ( -3y) Local maximums: Previevw Local minimums: Preview Saddle points: Preview For each classification, enter a list of ordered pairs (r, y) where the max/min/sac Get help: Video Points possible: 1 This is attempt 1 of 3. Submit Due in 9 Suppose that f(z, y) yy3 3y with D (, y) | 0 y 3) 1. The critical point of f(z, y)...
(1 point) Consider the wave equation 1(1)utt = uzz for-oo < z < oo, t>0 with initial conditions ut (z,0-0 and u(z,0) = /(z), where (2) f(z) = 1 for 0 < z < 1, (3) f(z) =-1 for-1 < z < 0, and (4) f(z) = 0 for all other. The slanting lines in the figure below show the characteristics for this PDE that originate on the z-axis at the points of discontinuity of the initial data f f(x)...
5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2 +3(2-1)2 Let EC R3 be the closed half-ball E = {(x, y, z) e R$: x² + y2 +< 9 and 2 >0}. Find all the points (x, y, z) at which f attains its global maximum and minimum on E.
11. (8 marks) Let F(x, y, z) = x'yz, where r, y,z E R and y, z 2 0. Execute the following steps to prove that F(z,y,2) < (y 11(a) Assume each of r, y, z is non-zero and so ryz= s, where s> 0. Prove that 3 F(e.y.) (y)( su, y su, z sw and refer back to Question (Hint: Set 10.) 11(b) Show that if r 0 or y0 or z 0, then F(z, y, z) ( 11(c)...
2.1 & 2.2 Finding relative max and min, inflection points and graphing Find all the critical values of f)--3)Which critical value gives a relative maximum? Which critical value gives a relative minimum? Find all the inflection points of f(x) 2 -2r +1,ga) Does the function g(r) Jrl have any critical value? Sketch a graph for f(x) such that f'(z) >0 over the intervals (-00,-2) and (2,4); f(a) < 0 over the intervals (-2,2) and (4, oo); f"()0 when 0, r...