Suppose that f(x) is a differentiable function such that the tangent line at x = 3...
Graph off 2. The figure above shows the graph of f', given by f'(x) = ln(x2+1) sin(x*) on the closed interval (0,3). The function f is twice differentiable with f(0) = 3. (a) Use the graph of f' to determine whether the graph of f concaves up or concaves down on the interval 0<x<1. Justify your answer. (6) On the closed interval (0,3), find the value of x at which f attains its absolute maximum Justify your answer. (c) Find...
Suppose f '(x)=x+ (x - 1). Then f '(x) = x (3x - 2). Over which interval(s) is the graph off both increasing and concave up? 1.x<0 Il. 0<x< II. <x<1 IV. * > 1 (A) I only (B) II only (C) II and IV (D) I and IV O (E) IY only Suppose f'(x) = x+ (x - 1). Then f"(x) = x (3x - 2). Over which interval(s) is the graph off both increasing and concave up? 1.x<0...
Suppose is a differentiable function of one variable. Show that all tangent planes to the surface z = y f(x/y) intersect at a common point.
3. (25 pts) Suppose f(x) is twice continuously differentiable for all r, and f"(x) > 0 for all , and f(x) has a root at p satisfying f'(p) < 0. Let p, be Newton's method's sequence of approximations for initial guess po < p. Prove pi > po and pı < p Remember, Newton's method is Pn+1 = pn - f(pn)/f'(P/) and 1 f"(En P+1 P2 f(pP-p)2. between pn and p for some 3. (25 pts) Suppose f(x) is twice...
The f function differentiable at (-1,4) and 7(3) = 5 also let Hx f'(x) > -1. Find the greatest value f(0).
Can someone help me? I am not very familiar with the Newton method. The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x)- 0 with initial approximationx-6. 이 (a) Draw the tangent lines that are used to find x2 and x3, and estimate the numerical values of x2 and x3. (Round your answers to one decimal place.) x2 = x3 = The figure shows the graph...
[3](4 pts) Let f(x) = u(x, y) + iv(x,y) be differentiable for all z = x + iy. If v(x, y) = x + xy + y2 – x2, for all (x, y), find u(x,y) and express f(x) explicitly in terms of z.
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
Find an equation for the tangent line to the graph of the given function at (4,23). f(x)=x2+7 Find an equation for the tangent line to the graph of f(x)-x+7at (4,23) y = Find an equation for the tangent line to the graph of the given function at (4,23). f(x)=x2+7 Find an equation for the tangent line to the graph of f(x)-x+7at (4,23) y =
35. f(z) (3z+5)5 f(x) = SK-53 x-2 x2 -2x 37. f*)-+1 In problems 54-61, find dy/dx. 54. xy'- xy+10 0 In problems 62-63, find the equation of the tangent line to the given graph at the given point. 62. yxy - 6 0 at the point (1,2) 63. x+xy - vy-3 0 at the point (1,4) In problems 64-78, find y for the equation. 35. f(z) (3z+5)5 f(x) = SK-53 x-2 x2 -2x 37. f*)-+1 In problems 54-61, find dy/dx....