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A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…
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Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?
A: As per our guidelines we are mandated to solve only one question at a time please repost the…
Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, 1]?
A: follow next step
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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]
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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]
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A: To Sketch: The graph of a function f that is continuous from x = 1 to x = 5 and has the given…
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Q: 4. Verify Rolle's Theorem for f(x) = x² - 2x +1 on [-1,3]
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Q: 21. Discuss the continuity of : 1 x+ - for x 2 (ans.: discontinuous at x-0,2 ; continuous at x-1)
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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, n]?
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- Consider the function f(a,b) = a+b-a^2-b^2-ab over a closed interval with the endpoints (0,0), (2,0), (2,2), and (0,2). Locate the critical point inside of this square and find the absolute max and min of f, and the points they happen at all 4 boundaries. Based on the calculations what's the absolute maximum and minimum of this region ? Please show all steps and explain throughly.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.the continuous function has a critical point. (a)Is the critical point a local maximum or a local minimum? (b)Sketch the graph near the critical point. Label the coordinates of the critical point. 1. f(1) = 5, f ′(1) = 0, f ″(1) = −2 2. h(2) = −5, h′(2) = 0, h″(2) = −4
- Find the critical points and determine if the function is increasing or decreasing at the given intervals. y=9x^4+2x^3 Left critical point: c1= ?????????Right critical point: c2= ??????? The function is:decrease or increase on (−∞,c1).decrease or increase on (c1,c2).decrease or increase on (c2,∞).(A) find the critical numbers of f, if any (B) find the open intervals on which the function is increasing or decreasing (C) apply the First Derivative Test to identify all relative extremaFind local maxima and minima and saddle points of the function f(x,y) = 3xy2+x3-3x2-3y2+2. Classify each critical point with 2nd derivative. Make a table with: the point value of the function value of discriminant value of second partial derivative with respect to x or y characterization
- A metal storage tank with fixed volume V0 = 360π m^3is to be constructed in the shape of a right circular cylinder (including the bottom) surmounted by a hemisphere. A picture is given below.What dimensions will require the least amount of metal? Show and organize your work; use the firstderivative test or the second derivative test or other tools to check that yours is the desired optimalsolution.ContinuousFind the area in square units of the region under the graph of the function f on the interval[-10,5] using the fundamental theorem of calculus then verify the result using geometry f(x) = 5