3. A function f(x) that you do not know has the following properties. (6 points total)...
Consider the function f(1) = 22 - 62+5 Answer all parts: (a) - (). (a) The vertex is (b) The axis of symmetry is (c) The 2-intercept(s) is (are) (Enter the list, separated by a comma. (d) The y-intercept is y = (e) Sketch a graph of f(x) = 22 - 61 +5. Instructions: To sketch the graph, click on the following locations: (1) vertex (2) the x--intercepts 10 10 0 -10 After graphing answer the following: (f) What is...
Let f (x) = x2 – 6 and g(x) = V6 – 2. Determine the domain of f (g(x)). O [-6,6] o [6,00) 0 (-00,-6] U [6,00) o(-00,00) 01-00,6] Determine the domain restriction, if one is necessary, so that f (x) = 212 + 1 is one-to-one. O [3,00) o(-0,3) O No restriction is necessary. O (1,00) O (3,00) Determine the vertex of the parabola described by f (x) = 3 – 12x + 2x2. O (2, -13) O (3,...
(5 points) A continuous function f, defined for all x, has the following properties: 1. f is decreasing 2. f is concave up 3. f(26) = -5 4. f'(26) = - Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in an...
f(x) is continuous on (-00,00) and has critical numbers at x = a, b, c, and d Use the sign chart for f'(x) to determine whether f has a local maximum, a local minimum, or neither at each critical number f'(x) + + + 0 + + + ND ND + + + 0 - h c d Does f(x) have a local minimum, a local maximum, or no local extremum atx=a? Choose the correct answer below. © A. no...
Sketch the graph of a continuous function on (-4,0 satisfying the given properties f')0 for x = -3 and - 2. f has an absolute maximum x 0;fhas an absolute minimum at Choose the correct graph below and has a local minimum at x-2
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
Sketch the graph of a function that has the following properties: a. Domain: all real numbers b. Range: all real numbers c. Intercepts: (0, -1) and (5,0) d. A local maximum value of -2 is at -1 e. A local minimum value of -6 is at 2 3.
12 consider the function f(x) = (1-x²) 1/3 over the interval [0,3]. a) The absolute maximum value of f over the interval is at x = B) The absolute minimum value off over the interval is at x=
The derivative of the function f(0) = 96x + 12x2 – 20x3 + 3x4 has three roots:-1, 2, and 4. That is, f'(-1) = f'(2) = f'(4) = 0 and there are no other points where f'(x) = 0. Find the maximum and the minimum value of f on the interval (0,3). Explain how you arrive at your answer.
(6 pts) 11) Find the absolute maximum and minimum of the function f(x) = x/9 - 22 on the interval (0,3] Give your final answers as (x,y) points.