12r45 20x3 - 9 and classify them using a graph Find the critical numbers of the function f(x) - + is a Neither a max or min is a Local Max is a Local Min 0 Get help: Video
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- 5) Given the function y = f(x) defined at all real values of x. Let x = 2, 3, 5 and 7 are critical numbers of the function. If f’(x) is positive on the intervals (-inf, 2) and (5,7) and f’(x) is negative on the intervals (2,3) and (3,5). Which of the following is true? A) f has a point of inflection with horizontal tangent at x=3 B) f has a relative maxima at x=5 C) f has a relative minima at x=2 D) none of the other choicesFind the critical point and determine if the function is increasing or decreasing on the given intervals.y=−x2+2x−6y=−x2+2x−6 Critical point: c=c= The function is: is the function Increasing or Decreasing on (−∞,c)(−∞,c). is the function Increasing or Decreasing on (c,∞)(c,∞).Let f(x)=x2−10x+6f(x)=x2−10x+6. Find the critical point cc of f(x)f(x) and compute f(c)f(c). The critical point cc is = The value of f(c)f(c) = Compute the value of f(x)f(x) at the endpoints of the interval [0,10][0,10]. f(0)f(0) = f(10)f(10) = Determine the min and max of f(x)f(x) on [0,10][0,10]. Minimum value = Maximum value = Find the extreme values of f(x)f(x) on [0,1][0,1]. Minimum value = Maximum value =
- Let f(x)=x^3-3x^2-24x+4 A)Find the critical numbers of f. B)Find the intervals on which f is increasing or decreasing. C)At what values of x, if any, does f have a local max or min value? D)Find the intervals of concavity and inflation points. Inflection point should be of the form (x,y)Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is y = 44t + 0.5t2 − t3, 0 ≤ t ≤ 6. (a) Find the critical values of this function. (Assume −∞ < t < ∞. Enter your answers as a comma-separated list.) t = (b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.) t = (c) For which values of t, for 0 ≤ t ≤ 6, is y increasing? (Enter your answer using interval notation.) (d) Graph this function. The t y-coordinate plane is given. The curve starts at the origin, goes up and right becoming more steep, passes through the approximate point (0.17, 7), goes up and right becoming less steep, changes direction at the point (4, 120), goes down and right becoming more steep, and ends in the first quadrant. The t y-coordinate plane is given. The curve starts at the origin, goes up and right becoming less steep, changes…Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is y = 24t + 0.5t2 − t3, 0 ≤ t ≤ 5. (a) Find the critical values of this function. (Assume −∞ < t < ∞. Enter your answers as a comma-separated list.) t = (b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.) t = (c) For which values of t, for 0 ≤ t ≤ 5, is y increasing? (Enter your answer using interval notation.)
- The critical points of f(x,y)=x3+4x2y+9xy2−9x are (0,−1), (0,1), (353–√5–√,−2153–√5–√), and (−353–√5–√,2153–√5–√) . Classify the critical points of f(x,y): a.The point (0,−1) is a: b.The point (0,1) is a : c.The point (353–√5–√,−2153–√5–√) is a d.The point (−353–√5–√,2153–√5–√) is aLet f(x)=(x+e2020)∣x2−e4040∣. Find the correct answers. The total number of critical points Number of critical points where f′ is zero] Let f(x)=x^-2ln(x).a) Find the critical number(s) of the function f.b) Find the absolute maximum and minimum values, if any, of f on the given interval [1/2,4]
- a function is defined on the closed interval[-4,8] consists of two linear pieces and a semi circle defined by f(x)=3x integral from 0 to x g(t) dt find f(7) and f'(7) and find the value of x in the closed interval[-4,] at which f attains its maximum value. Justify your answerConsider the function f(x) = x3 + x2 − x + 9 on the interval [−3, 0]. a. Find f '(x). b. Find the critical value of f(x) on the interval [−3, 0]. c. Evaluate the function at the critical value. d. Evaluate the function at the endpoints of the given interval. e. Find the absolute maxima and minima for f(x) on the interval [−3, 0].nvestigate the one-parameter family of functions. Assume that a is positive. f(x)=x−ax Select the response which shows the correct: • graph of f(x) using three different values for a, • description of the critical points of f and how they appear to move as a increases, • x-coordinates of the critical point(s) of f in terms of a.