1. [7 Marks] For the following function f(x)= x4 – 2x3 - 5 Determine the Inflection...
1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points ONLY 2.. For the given sketch of y = :) Find the intersection points A, B and C. (Do not Estimate!) +2, y=x+2= ii) Determine the shaded area enclosed between the given two curves -*+2, y =x +2
1. .] For the following function f(x)= x* – 2x - 5 Determine the Inflection Points ONLY 2. For the given sketch of y i) Find the intersection points A, B and C. (Do not Estimate!) ***2, y =x +2; ii) Determine the shaded area enclosed between the given two curves y =*+2, y=x+2
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f. b) determine the interval(s) on which the graph off is increasing c) find f"(x) and the x-coordinates of the possible inflection points d) determine the interval(s) on which the graph off is concave down.
Consider the following. f(x) = 1 4 x4 + 1 2 x3 − 3x2 + 4 Find f '(x). f '(x) = x3+ 3x2 2−6x Find f ''(x). f ''(x) = 3x2+3x−6 Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) x = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using...
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determine lim sinand the behavior of the graph near zero. 5. Using your graphing calculator sketch h(x)-x4-2x3 over [-2,2] below, find the critical values and on the graph label the coordinates of any local, global(absolute) minima, maxima or point of inflection on the sketch,...
7. List the intervals of concavity and the inflection point(s) for the following function. If there are none write NA. f(x) = x4 – 4x3 Intervals on which f is Concave Up: Intervals on which f is Concave Down: Inflection Point(s) (ordered pair):_
2. (a) Obtain and classify all stationary points and point of inflection of the function f(x) = 4x3 – 22x2 + 40x – 25. [5 marks) (b) Sketch the function y = f(x) showing all x and y intercepts, stationary points and point of inflection. One of the factors of f(x) = 423 – 22cr2 + 40x – 25 is (r – ). [2 marks] (c) Evaluate the definite integral of f(c) on the domain 2 € (0,6]. [3 marks)
Question 2: 60 Marks The function fx)-x-2x3-5x2+12x -5 as four distinct roots, we want to determine the roots by means of Müller's method (2.1) Which option is false? (10) (1) f(x) x-2x3-5x 12x-5 has no singularities and no obvious symmetries and f(0)--5 (2) f(x) 4x3 6x2-10x 12, f(x) 12x2 - 12x (3) f"(x) has a local ertremum at X = 0.5 (4) the two zeros for f"(x) are -0.5408 and 1.5408 (5) f"(x) has a local marinum at X =...
a. 4. Let h(x) = x4 – 6x3 + 12x2. Find h'(x) and h"(x). b. Find the open intervals on which h is concave upward and concave downward. Give the points of inflection for h as ordered pairs. c. a. 5. Let g(x) = x4 – 2x3 + 3. x3 This function is defined, differentiable, for all real numbers except x = where g has a vertical asymptote. b. Find g'(x), given any other value of x. c. Suppose we...
Find the inflection points of f(x)=x4+x3−3x2+8. Enter the exact answers in increasing order. x= x=