. Consider the function f(x) = 2x^ 3 + 9x^ 2 − 24x + 1. (1) (5 points) Find all the critical points of f(x). (2) (5 points) Find the intervals on which f(x) is increasing and decreasing, and find the x-values of any relative minima/maxima.
7. Suppose X and Y have joint pdf f(x,y) = 24x y if x >0, y>0,x+y<1 and 0 otherwise. Find P(Y > 2x).
Find f. f''(x) = – 2 + 24x – 12x, f(0) = 2, f'(0) = 12 f(x) = Preview
Find the inflection point(s) of the function f (x) = 2:03 + 15x2 + 24x O Inflection point at ( -,5). No inflection points. Inflection points at (-1,-11) and (-4,16). Inflection point at (0,0).
14. Suppose that f(x) is continuous on (60,-) Given the graph y = f'(x) below, find the following: y = f'(x) In (None may be an answer): Find the number lines of f'&f" 1. relative maximumat x= 2. relative minimum at x= 3. The graph of y=f(x) has points of inflection at x= -&x= (Enter a number from smallest to largest x-value.)
What is the value of xwhen f(x) = -1 1) 3 2) -1 3) 5 14 4 o
[3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that \f'(x) < 1/(1 - 1z| for all z e D[0, 1]. [3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that f'(x) < 1/(1-1-12 for all z e D[0, 1]
Solve the problem. 14) Suppose that f(x)- 4 +3. What is f(6)? What point is on the graph of f?
1. For a function f(x) (not shown), we have the graphs of f' (x), f ''(x) and f '''(x). Use these graphs to answer the following questions. The difference between a level 1 and 2 pass will be in the number of correct answers and your attention to detail. 1a. Identify all intervals, approximately, where the original function, f(x) is increasing 1b. Identify all intervals, approximately, where the original function f(x) is decreasing. 1c. Identify all intervals, approximately, where the...
Suppose that f(x, y) = 1 on the domain D = {(x, y) – 5 < x < 3, -5 <y <3}. D a Then the double integral of f(x, y) over D is 1 dædy