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Q: prove: f(x)=5x is continuous at x=2 note: please prove this in theorem format(two columns)
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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?The continuous function has exactly one critical point. Find the x-values at which the global maximum and the global minimum occur in the interval 2 is less then or equal to x which is less then or equal to 8 h'(4)is undefined, h'(x) = -1 for x < 4 and h'(x) = 1 for x>x the global maximum occurs when x = the global minimum occurs when x =Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is an arbitrary positive integer, find points x1 and x2 (int terms of n) in the interval(-1/n, 1/n( such that g(x2) = 1 and g(x2) = -1. d) Explain (in a brief paragraph) why (c) implies that g does not have a limit at x = 0. e) Where is g continuous? Justify your answer. You may use facts from the textbook in Section 2.2 - 2.5.
- Sketch the graph of a function that is continuous on [0, 10], differentiable on (0, 10), that satisfies the following properties. a. has 7 critical points.b. has 2 relative maxima, none of which are absolute maxima. c. has 3 relative minima, one of which is an absolute maximum.Label all critical points, relative extrema, absolute extrema, and inflection points.true or false questions . but please explain why. important 1- for all functions y=f(x) defined on [0,1], the set (f[0,1]) is a bounded set 2- all functions that are continuous on (0,1] are bounded 3- if y=f(x) is an increasing function on the interval (a,b), and the set {f(x):a<x<b} is also an interval, then y=f(x) is continuous on (a,b) 4- if f:R->{0,1} and I is an interval on which f has both values, then f has a discontinuity in I . 5- if the limit of a function at x=c is 5 , then f(c)=5 6- the function y=f(x) is defined as follows: f(x)=3+ [sin(x-2)/(x-2)] if x≠2 and f(2)=4. then y=f(x) is continuous at all real numbers x.True False Suppose a stationary police officer at point A sees you pass by at 5:10pm and his colleague 10 Miles down the road at point B sees you pass at 5:16pm. The speed limit is 65MPH between point A and point B. They can then prove you must have broken the speed limit at some point between A and B. You may assume that your position as a function of time is both continuous and dirferentiable everywhere. Your justification should cite a theorem.
- What values of a and b make f(x)=x^3+ax^2+bx have Part 1 a. For a local maximum at x=−3 and a local minimum at x=7, a= ______ and b=_______. Part 2 b. For a local minimum at x=8 and a point of inflection at x=2, a= _______ and b= ______.Find the exact location of all the relative and absolute extrema of the function. (Order your answers from smallest to largest x.) f(x) = 3x2 − 12x + 3 with domain [0, 3] f has ---Select--- a relative minimum a relative maximum an absolute minimum an absolute maximum no extremum at (x, y) = 0,3 . f has ---Select--- a relative minimum a relative maximum an absolute minimum an absolute maximum no extremum at (x, y) = . f has ---Select--- a relative minimum a relative maximum an absolute minimum an absolute maximum no extremum at (x, y) = .Sketch the graph of a function f that is continuous on [1,5] and has the given properties. Absolute minimum at 3 absolute maximum at 4 local minimum at 2 Could you please show it step by step? thank you!
- If a function f is differentiable on [7,11], then which of the following statements must be true? The absolute maximum value is f(11). f has an absolute maximum value on [7,11]. There is a tangent line (to graph of f) over (7,11), which is parallel to the secant line of f at x=7 and x=11. f has an absolute minimum value on (7,11). f is continuous on [7,11].The graph of a function f is shown. The x y-coordinate plane is given. The curve begins at y = 1 on the positive y-axis, appears to go horizontally right, passes through the approximate point (3, 1), goes up and right becoming more steep, and ends at the point (5, 3) nearly vertical. Does f satisfy the hypotheses of the Mean Value Theorem on the interval [0, 5]? Yes, because f is continuous on the open interval (0, 5) and differentiable on the closed interval [0, 5].Yes, because f is increasing on closed interval [0, 5]. Yes, because f is continuous on the closed interval [0, 5] and differentiable on the open interval (0, 5).No, because f is not differentiable on the open interval (0, 5).No, because f does not have a minimum nor a maximum on the closed interval [0, 5].No, because f is not continuous on the open interval (0, 5). If so, find a value c that satisfies the conclusion of the Mean Value Theorem on that interval. (If an answer does not exist, enter DNE.) c = 3Please help me found the characteristics of this function in the given image. Please answer these I dont want to re ask them again. The form of the function: The original ordinate is: Number of abscissas originally: The zeros of the function are: Maximum local: Local minimum: When x ->-∞, f(x) ->: When x -> ∞, f(x) ->: Field: Image: The function is increasing when: the function is decreasing when: