Let f(x) = 3x − 3x^2 . Show that 2/3 is an attracting fixed point. Graphical analysis is not sufficient.
Let f(x) = 3x − 3x^2 . Show that 2/3 is an attracting fixed point. Graphical...
Let f be the polynomial f()25. Show that f has a parabolic fixed point at the origin, and that f2 has a multiple fixed point at the origin. By calculating fo2, show that f has 4 attracting petals. Let f be the polynomial f()25. Show that f has a parabolic fixed point at the origin, and that f2 has a multiple fixed point at the origin. By calculating fo2, show that f has 4 attracting petals.
(a) Let f(x) = 3x – 2. Show that f'(x) = 3 using the definition of the derivative as a limit (Definition 21.1.2). 1 (b) Let g(x) = ? . Show that y that -1 g'(x) = (x - 2)2 using the definition of the derivative as a limit (Definition 21.1.2).
1. Draw the orbit analysis or phase portrait of f(x) = x3 - X. 2. Find the neutral fixed point of g(x) = x - *3. Use graphical analysis to determine if the fixed point is weakly attracting, weakly repelling, or neither.
2a², where [Fixed Point Iterations, 15 pts). Let g(2) = -22 + 3x + a a is a parameter. (a) Show that a is a fixed point of g(x). (b) For what values of a does the iteration scheme On+1 = g(n) converge linearly to the fixed point a (provided zo is chosen sufficiently close to a)? (c) Is there a value of a for which convergence is quadratic?
Let f(x) = 3x + 2 and g(x) 3x + 2 and g(x) = 4x2 + 2x. After simplifying, (fog)(x) =
3x + 4 for x 2 12. Let (x) 2-x for -1 <x51 . Find f(1/3) and (3/2). Sketch the graph of the -3x for x S-1 function. Determine the domain and range. (2,2,5, 3, and 3 points)
(1 1 point) Let F(x) = 5 9 dt, for > 9. In(3) A. F'(2) 9/(In(3x)) B. On what interval or intervals is Fincreasing? те (Give your answer as an interval or a list of intervals, e.g., (-infinity, 8] or (1,5),(7,10), or enter none for no intervals.) c. On what interval or intervals is the graph of F concave up? CE (Give your answer as an interval or a list of intervals, e.g., (-infinity, 8] or (1,5),(7,10), or enter none...
Let f : R^2 \rightarrow R be given by f(x,y)=x^3-3xy^2. Let p = (0.0) Show that p is an isolated critical point of f show that p is a degenerate critical point. show that The index of grad f at p is equal to -2
0 let f(x)= 3x²+x+2 a) Approximate the area under f(x) from x=o to x=3 by computing
Let f(x) = x 3 _ 3x² a) The interval(s) on which the function is increasing and the intervalls) on which the function f is decreasing B) The relative maximum value of f is and the relative minimum value of f is c) The intervalls) on which the function of is and the intervalls) on concave up which the function F is concare down D) The inflection Point(s) off