1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points...
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
1. [7 Marks] For the following function f(x)= x4 – 2x3 - 5 Determine the Inflection Points ONLY
2. [18 Marks] For the given sketch of y = +2, y = x +2. 1) Find the intersection points A, B and C. (Do not Estimate!) 4 [7 Marks) B 15FMAT127 Assignment 2 Page 2 of 3 [11 Marks) ii) Determine the shaded area enclosed between the given two curves x3 y = +2, y = x +2 15FMAT127 Assignment 2 Page 3 of 3
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 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 figure below. f(x) = 2x – x2 g(x) = x2 - 6x 81x) -10 (a) For the shaded region, find the points of intersection of the curves. (x, y) = ( 0,0 ) (smaller x-value) (x, y) = ( 4,-8 ) (larger x-value) (b) Form the integral that represents the area of the shaded region. dx (c) Find the area of the shaded region.
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)
[11 Marks) ii) Determine the shaded area enclosed between the given two curves 3 +2, y = x + 2 4 y =
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5) Hint: Do not expand! Instead use the product and chain rules then factor 2. (12 points) Find the absolute extrema of f(x) = on (-1,2). Give your answers as (x,y) points. Hint: It is much easier to take the derivative of f(x) by rewriting as f(x) = (1 + x4)-1 and use the chain rule 3. f(x) = ? - 7x + 1 (a)...
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,...